Mathematics · Textbook solutions
Probability
Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 70 questions
14.1 Probability — A Theoretical Approach
70 q
Solved Examples
Worked · 13
- 14.1 Eg.1Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.
- 14.1 Eg.2A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the (i) yellow ball? (ii) red ball? (iii) blue ball?
- 14.1 Eg.3Suppose we throw a die once. (i) What is the probability of getting a number greater than 4? (ii) What is the probability of getting a number less than or equal to 4?
- 14.1 Eg.4One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will (i) be an ace, (ii) not be an ace.
- 14.1 Eg.5Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match?
- 14.1 Eg.6Savita and Hamida are friends. What is the probability that both will have (i) different birthdays? (ii) the same birthday? (ignoring a leap year).
- 14.1 Eg.7There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?
- 14.1 Eg.8A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be (i) white? (ii) blue? (iii) red?
- 14.1 Eg.9Harpreet tosses two different coins simultaneously (say, one is of ₹1 and other of ₹2). What is the probability that she gets at least one head?
- 14.1 Eg.10(Marked in the book "Not from the examination point of view".) In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half-minute after starting?
- 14.1 Eg.11(Marked in the book "Not from the examination point of view".) A missing helicopter is reported to have crashed somewhere in the rectangular region shown in Fig. 14.2. What is the probability that it crashed inside the lake shown in the figure?
- 14.1 Eg.12A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that (i) it is acceptable to Jimmy? (ii) it is acceptable to Sujatha?
- 14.1 Eg.13Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is (i) 8? (ii) 13? (iii) less than or equal to 12?
Exercise 14.1
Practice · 57
- Complete the following statements:Ex 14.1 Q1 (i)Probability of an event E + Probability of the event 'not E' = __________ .
- Ex 14.1 Q1 (ii)The probability of an event that cannot happen is __________ . Such an event is called __________ .
- Ex 14.1 Q1 (iii)The probability of an event that is certain to happen is __________ . Such an event is called __________ .
- Ex 14.1 Q1 (iv)The sum of the probabilities of all the elementary events of an experiment is __________ .
- Ex 14.1 Q1 (v)The probability of an event is greater than or equal to __________ and less than or equal to __________ .
- Which of the following experiments have equally likely outcomes? Explain.Ex 14.1 Q2 (i)A driver attempts to start a car. The car starts or does not start.
- Ex 14.1 Q2 (ii)A player attempts to shoot a basketball. She/he shoots or misses the shot.
- Ex 14.1 Q2 (iii)A trial is made to answer a true-false question. The answer is right or wrong.
- Ex 14.1 Q2 (iv)A baby is born. It is a boy or a girl.
- Ex 14.1 Q3Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?
- Ex 14.1 Q4Which of the following cannot be the probability of an event?
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- Ex 14.1 Q5If P(E) = 0.05, what is the probability of 'not E'?
- A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes outEx 14.1 Q6 (i)an orange flavoured candy?
- Ex 14.1 Q6 (ii)a lemon flavoured candy?
- Ex 14.1 Q7It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
- A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn isEx 14.1 Q8 (i)red?
- Ex 14.1 Q8 (ii)not red?
- A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will beEx 14.1 Q9 (i)red?
- Ex 14.1 Q9 (ii)white?
- Ex 14.1 Q9 (iii)not green?
- A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coinEx 14.1 Q10 (i)will be a 50 p coin?
- Ex 14.1 Q10 (ii)will not be a ₹5 coin?
- Ex 14.1 Q11Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Fig. 14.4). What is the probability that the fish taken out is a male fish?
- A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig. 14.5), and these are equally likely outcomes. What is the probability that it will point atEx 14.1 Q12 (i)8?
- Ex 14.1 Q12 (ii)an odd number?
- Ex 14.1 Q12 (iii)a number greater than 2?
- Ex 14.1 Q12 (iv)a number less than 9?
- A die is thrown once. Find the probability of gettingEx 14.1 Q13 (i)a prime number;
- Ex 14.1 Q13 (ii)a number lying between 2 and 6;
- Ex 14.1 Q13 (iii)an odd number.
- One card is drawn from a well-shuffled deck of 52 cards. Find the probability of gettingEx 14.1 Q14 (i)a king of red colour
- Ex 14.1 Q14 (ii)a face card
- Ex 14.1 Q14 (iii)a red face card
- Ex 14.1 Q14 (iv)the jack of hearts
- Ex 14.1 Q14 (v)a spade
- Ex 14.1 Q14 (vi)the queen of diamonds
- Five cards — the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.Ex 14.1 Q15 (i)What is the probability that the card is the queen?
- Ex 14.1 Q15 (ii) (a)an ace?
- Ex 14.1 Q15 (ii) (b)a queen?
- Ex 14.1 Q1612 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
- A lot of 20 bulbs contain 4 defective ones.Ex 14.1 Q17 (i)One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
- Ex 14.1 Q17 (ii)Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?
- A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bearsEx 14.1 Q18 (i)a two-digit number
- Ex 14.1 Q18 (ii)a perfect square number
- Ex 14.1 Q18 (iii)a number divisible by 5
- A child has a die whose six faces show the letters A, B, C, D, E, A. The die is thrown once. What is the probability of gettingEx 14.1 Q19 (i)A?
- Ex 14.1 Q19 (ii)D?
- Ex 14.1 Q20(Marked in the book "Not from the examination point of view".) Suppose you drop a die at random on the rectangular region shown in Fig. 14.6. What is the probability that it will land inside the circle with diameter 1 m?
- A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability thatEx 14.1 Q21 (i)She will buy it?
- Ex 14.1 Q21 (ii)She will not buy it?
- Refer to Example 13 — two dice, one blue and one grey, are thrown at the same time.Ex 14.1 Q22 (i)Complete the following table:
Event : 'Sum on 2 dice' 2 3 4 5 6 7 8 9 10 11 12 Probability - Ex 14.1 Q22 (ii)A student argues that 'there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability . Do you agree with this argument? Justify your answer.
- Ex 14.1 Q23A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
- A die is thrown twice. What is the probability that [Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]Ex 14.1 Q24 (i)5 will not come up either time?
- Ex 14.1 Q24 (ii)5 will come up at least once?
- Which of the following arguments are correct and which are not correct? Give reasons for your answer.Ex 14.1 Q25 (i)If two coins are tossed simultaneously there are three possible outcomes — two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is .
- Ex 14.1 Q25 (ii)If a die is thrown, there are two possible outcomes — an odd number or an even number. Therefore, the probability of getting an odd number is .
What the board has asked from this chapter
Questions per paper · 63 papers · 2023 to 2026
2023: 2.3 questions per paper. 2024: 2.1 questions per paper. 2025: 2.1 questions per paper. 2026: 1.5 questions per paper
2026
23 q
- 4For an event E, , then the value of is :
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Sure, Impossible and Complementary Events - 5Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by 6, is :
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Probability with Cards, Dice and Coins - 9Three coins are tossed together. The probability of getting exactly one head, is :
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Probability with Cards, Dice and Coins - 10Which of the following can not be the probability of an event ?
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Sure, Impossible and Complementary Events - 10Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is
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Probability with Cards, Dice and Coins - 11A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is either a ten or a king is
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Probability with Cards, Dice and Coins - 16Meena calculates that the probability of her winning the first prize in a lottery is 0.08. If total 800 tickets were sold, the number of tickets bought by her, is
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Theoretical Probability and Elementary Events - 17Two dice are rolled together. The probability that sum of the numbers obtained is atmost 12, is
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Probability with Cards, Dice and Coins - 18Two dice are rolled together. The probability of getting an outcome where , is
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Probability with Cards, Dice and Coins - 18The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is :
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Probability from a Collection of Objects - 18A die is thrown once. Probability of getting a number other than 3 is :
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Sure, Impossible and Complementary Events - Question Numbers 19 and 20 are Assertion (A) and Reason (R) based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options (A), (B), (C) and (D) as given below :19Assertion (A) : If probability of happening of an event is , , then p can't be more than 5. Reason (R) : for an event E.
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Sure, Impossible and Complementary Events - Question numbers 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below :19Assertion (A) : The probability that a leap year has 53 Mondays is . Reason (R) : The probability that a non-leap year has 53 Mondays is .
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Theoretical Probability and Elementary Events - 25A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is , then find the number of yellow balls.Probability from a Collection of Objects
- 30Two different dice are thrown together. Find the probability that the numbers obtained have : (i) even sum, (ii) even product.Probability with Cards, Dice and Coins
- 29Two different coins are tossed simultaneously. What is the probability of getting : (i) at least one head ? (ii) at most one tail ? (iii) a head and a tail ?Probability with Cards, Dice and Coins
- 30A bag contains 30 balls out of which 'm' number of balls are blue in colour. (i) Find the probability that a ball drawn at random from the bag is not blue. (ii) If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be times the probability of drawing a blue ball in the first case. Find the value of m.Probability from a Collection of Objects
- 31Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that : (i) same number appears on both the dice ? (ii) different number appears on both the dice ?Probability with Cards, Dice and Coins
- 31Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.Probability with Cards, Dice and Coins
- A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :37 (i)Find the probability that the drawn card is a face card.Probability with Cards, Dice and Coins
- A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :37 (ii)Find the probability that the drawn card is either a king or a queen.Probability with Cards, Dice and Coins
- A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :37 (iii) (a)Do you think that the probability of getting a queen was higher if none of the cards were dropped ? Justify your answer.Probability with Cards, Dice and Coins
- A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :37 (iii) (b)Find the probability that the drawn card is a jack. Compare it with the probability when none of the cards were dropped. In which case is the probability of getting a jack higher ?Probability with Cards, Dice and Coins
2025
38 q
- 1If for any event E, , then the value of is :
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Sure, Impossible and Complementary Events - 2A pair of dice is thrown once. The probability that sum of numbers appearing on top faces is at least 4 is :
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Probability with Cards, Dice and Coins - 2The probability of drawing an even prime number out of numbers from 1 to 30 is :
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Probability from a Collection of Objects - 5The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a red ball at random from this bag is , then the total number of balls in the bag is :
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Probability from a Collection of Objects - 6If in a lottery, there are 10 prizes and 30 blanks, then the probability of winning a prize is :
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Probability from a Collection of Objects - 7A bag contains red balls and black balls in the ratio 3 : 7. A ball is drawn at random. The probability that ball so drawn is black in colour, is
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Probability from a Collection of Objects - 8Two coins are tossed simultaneously. The probability of getting atleast one head is
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Probability with Cards, Dice and Coins - 9A piggy bank contains ₹ 1 coins and ₹ 2 coins in the ratio 9 : 11 respectively. The piggy bank is accidently dropped and a coin pops out of it. The probability that it is a ₹ 2 coin is
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Probability from a Collection of Objects - 9Letters A to F are mentioned on six faces of a die such that each face has a different letter. Two such dice are thrown simultaneously. The probability that vowels turn up on both the dice is :
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Probability with Cards, Dice and Coins - 11In a cricket match, a batsman hits the boundary 7 times out of the 42 balls he plays. The probability of his not hitting a boundary is :
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Sure, Impossible and Complementary Events - 13If all the red face cards are removed from the deck of 52 playing cards, then the probability of getting a black jack from the remaining cards is :
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Probability with Cards, Dice and Coins - 13A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is :
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Probability with Cards, Dice and Coins - 14A die is thrown once. The probability of getting a number which is not a factor of 36, is :
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Probability with Cards, Dice and Coins - 16A bag contains red coloured, blue coloured and green coloured balls in the ratio 2 : 3 : 4. A ball is drawn at random from the given bag. The probability that the ball so drawn being not of blue colour is
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Probability from a Collection of Objects - 18The probability of getting a composite number greater than 3 on throwing a die is
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Probability with Cards, Dice and Coins - 18A pair of dice is thrown. The probability that sum of numbers appearing on top faces is at most 10 is :
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Probability with Cards, Dice and Coins - 18A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a spade or a king ?
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Probability with Cards, Dice and Coins - Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.19Assertion (A) : The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R) : For any event E, if P(E) = 1, then E is called a sure event.
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Sure, Impossible and Complementary Events - Directions : In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option from the following :20In an experiment of throwing a die, Assertion (A) : Event : getting a number less than 3 and Event : getting a number greater than 3 are complementary events. Reason (R) : If two events E and F are complementary events, then .
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Sure, Impossible and Complementary Events - 22All the face cards are removed from the pack of 52 cards and a card is drawn at random from the remaining cards. Find the probability that the card so drawn is (i) a spade. (ii) not an ace.Probability with Cards, Dice and Coins
- 22A bag contains cards which are numbered from 5 to 100 such that each card bears a different number. A card is drawn at random. Find the probability that number on the card is (i) a perfect square (ii) a 2-digit numberProbability from a Collection of Objects
- 22The probability of guessing the correct answer of a certain test question is . If the probability of not guessing the correct answer is , then find the value of x.Sure, Impossible and Complementary Events
- 22Saima and Aryaa were born in the month of June in the year 2012. Find the probability that : (i) they have different dates of birth. (ii) they have same date of birth.Theoretical Probability and Elementary Events
- 24A bag contains balls numbered 2 to 91 such that each ball bears a different number. A ball is drawn at random from the bag. Find the probability that (i) it bears a 2– digit number (ii) it bears a multiple of 1.Probability from a Collection of Objects
- 24From a pack of 52 cards, all aces and all kings are removed. A card is drawn at random from the remaining cards. Find the probability that the card so drawn is (i) a face card. (ii) a card of red colour.Probability with Cards, Dice and Coins
- 24Renu and Simran were born in the year 2000 which is a leap year. Find the probability that : (i) both have same birthday. (ii) both have different birthdays.Theoretical Probability and Elementary Events
- 25While shuffling a pack of 52 cards, one card was accidently dropped. Find the probability that the dropped card (i) is not a face card. (ii) is a black king.Probability with Cards, Dice and Coins
- 25Two friends Anil and Ashraf were born in the December month in the year 2010. Find the probability that : (i) they share same date of birth. (ii) they have different dates of birth.Theoretical Probability and Elementary Events
- 25The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is , find the total number of balls in the given bag.Probability from a Collection of Objects
- 26All face cards of spades are removed from a pack of 52 playing cards and the remaining pack is shuffled well. A card is then drawn at random from the remaining pack. Find the probability of getting : (a) a face card (b) an ace or a jackProbability with Cards, Dice and Coins
- 27If 65% of the population has black eyes, 25% have brown eyes and the remaining have blue eyes, what is the probability that a person selected at random has : (a) blue eyes ? (b) brown or black eyes ?Sure, Impossible and Complementary Events
- 27Two dice are rolled together. Find the probability of getting : (i) a multiple of 2 on one and a multiple of 3 on the other die. (ii) the product of two numbers on the top of the two dice is a perfect square number.Probability with Cards, Dice and Coins
- 30Three unbiased coins are tossed simultaneously. Find the probability of getting : (a) exactly two tails (b) at least one head (c) at most two headsProbability with Cards, Dice and Coins
- 31Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.Probability with Cards, Dice and Coins
- Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose. Answer the following questions if Rahul draws a card today :37 (i)What is the probability that Rahul draws a card with an even number ?Probability from a Collection of Objects
- Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose. Answer the following questions if Rahul draws a card today :37 (ii)What is the probability that Rahul draws a card with an odd number less than 30 ?Probability from a Collection of Objects
- Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose. Answer the following questions if Rahul draws a card today :37 (iii) (a)What is the probability that Rahul draws a card with a prime number between 50 and 74 ?Probability from a Collection of Objects
- Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose. Answer the following questions if Rahul draws a card today :37 (iii) (b)What is the probability that Rahul draws a card with an even number divisible by 5 ?Probability from a Collection of Objects
2024
32 q
- 1A bag contains 3 red balls, 5 white balls and 7 black balls. The probability that a ball drawn from the bag at random will be neither red nor black is :
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Probability from a Collection of Objects - 2The probability of getting a bad egg in a lot of 400 eggs is 0.045. The number of good eggs in the lot is :
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Sure, Impossible and Complementary Events - 2If the probability of a player winning a game is 0.79, then the probability of his losing the same game is :
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Sure, Impossible and Complementary Events - 3Two dice are thrown together. The probability that they show different numbers is :
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Probability with Cards, Dice and Coins - 4The probability of guessing the correct answer to a certain test question is . If the probability of not guessing the correct answer to this question is , then the value of is :
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Sure, Impossible and Complementary Events - 7Which of the following is not probability of an event ?
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Sure, Impossible and Complementary Events - 7One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is :
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Probability from a Collection of Objects - 7One card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is a red ace card, is :
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Probability with Cards, Dice and Coins - 8Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is
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Probability with Cards, Dice and Coins - 8From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is :
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Probability from a Collection of Objects - 8Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is :
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Probability with Cards, Dice and Coins - 10Two coins are tossed simultaneously. The probability of getting at most one tail is :
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Probability with Cards, Dice and Coins - 11What is the probability that a number selected randomly from the numbers is a multiple of 4 ?
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Probability from a Collection of Objects - 13A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is
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Probability from a Collection of Objects - 15From the letters of the word “MOBILE”, a letter is selected at random. The probability that the selected letter is a vowel, is :
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Theoretical Probability and Elementary Events - 15If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9; then the probability that this digit is an odd prime number is :
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Probability from a Collection of Objects - 16Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3 or 5, is :
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Probability with Cards, Dice and Coins - 16The probability of throwing a number greater than 2 with a fair die is :
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Probability with Cards, Dice and Coins - 17For an event E, if , then the value of is :
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Sure, Impossible and Complementary Events - Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below :20Assertion (A) : In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is . Reason (R) :
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Sure, Impossible and Complementary Events - 21The king, queen and ace of clubs and diamonds are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is randomly drawn from the remaining cards. Find the probability of getting (i) a card of clubs. (ii) a red coloured card.Probability with Cards, Dice and Coins
- 21One card is drawn at random from a well shuffled deck of 52 cards. Find the probability that the card drawn (i) is queen of hearts; (ii) is not a jack.Probability with Cards, Dice and Coins
- 22In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card.Probability with Cards, Dice and Coins
- 25A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam, a trader, will accept the shirts which are good but Anmol, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. Find the probability that it is acceptable to Anmol.Probability from a Collection of Objects
- 27 (a)Three coins are tossed simultaneously. What is the probability of getting (i) at least one head ? (ii) exactly two tails ? (iii) at most one tail ?Probability with Cards, Dice and Coins
- 27 (b)A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a : (i) 2-digit number less than 40. (ii) number divisible by 5 and greater than 50. (iii) a perfect square number.Probability from a Collection of Objects
- 30Three unbiased coins are tossed simultaneously. Find the probability of getting : (i) at least one head. (ii) exactly one tail. (iii) two heads and one tail.Probability with Cards, Dice and Coins
- 31A jar contains 54 marbles, each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is , and the probability of selecting a green marble at random is . How many white marbles does this jar contain ?Probability from a Collection of Objects
- BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.Based on the above information, answer the following :
Numbers announced Number of times 0-15 8 15-30 9 30-45 10 45-60 12 60-75 9 37 (ii)When first ball was picked up, what was the probability of calling out an even number ?Probability from a Collection of Objects - In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey. Observe the pie chart and answer the following questions :38 (i)If one person is selected at random, find the probability that he/she travelled by bus or ship.Probability from a Collection of Objects
- In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey. Observe the pie chart and answer the following questions :38 (iii) (a)A person is selected at random. If the probability that he did not use train is , find the number of people who used train.Sure, Impossible and Complementary Events
- In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey. Observe the pie chart and answer the following questions :38 (iii) (b)The probability that randomly selected person used aeroplane is . Find the revenue collected by air company at the rate of ₹ 5,000 per person.Probability from a Collection of Objects
2023
34 q
- 2In a lottery, there are 5 prizes and 20 blanks. The probability of getting a prize is :
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Probability from a Collection of Objects - 4Two dice are rolled together. What is the probability of getting a sum greater than 10 ?
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Probability with Cards, Dice and Coins - 6One card is drawn at random from a well shuffled pack of 52 playing cards. The probability that the drawn card is a queen, is :
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Probability with Cards, Dice and Coins - 7A bag contains 100 cards numbered 1 to 100. A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube ?
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Probability from a Collection of Objects - 11If three coins are tossed simultaneously, what is the probability of getting at most one tail ?
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Probability with Cards, Dice and Coins - 11A bag contains 5 pink, 8 blue and 7 yellow balls. One ball is drawn at random from the bag. What is the probability of getting neither a blue nor a pink ball ?
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Probability from a Collection of Objects - 11In a single throw of two dice, the probability of getting 12 as a product of two numbers obtained is :
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Probability with Cards, Dice and Coins - 11Two dice are thrown together. The probability of getting the difference of numbers on their upper faces equals to 3 is :
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Probability with Cards, Dice and Coins - 14A bag contains 5 red balls and green balls. If the probability of drawing a green ball is three times that of a red ball, then the value of is :
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Probability from a Collection of Objects - 15Two coins are tossed together. The probability of getting at least one tail is :
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Probability with Cards, Dice and Coins - 15A card is drawn at random from a well shuffled deck of 52 playing cards. The probability of getting a face card is
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Probability with Cards, Dice and Coins - 16In a survey, it is found that every fifth person has a vehicle. The probability of a person NOT having a vehicle, is
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Sure, Impossible and Complementary Events - 16Probability of happening of an event is denoted by p and probability of non-happening of the event is denoted by q. Relation between p and q is
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Sure, Impossible and Complementary Events - 16A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23 is
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Probability from a Collection of Objects - 17A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought ?
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Probability from a Collection of Objects - 17Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out of the bag at random. What is the probability that the number on the card taken out is an even number ?
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Probability from a Collection of Objects - 17Which of the following numbers *cannot* be the probability of happening of an event ?
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Sure, Impossible and Complementary Events - 18A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card drawn is not an ace is :
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Probability with Cards, Dice and Coins - 18In a group of 20 people, 5 can't swim. If one person is selected at random, then the probability that he/she can swim, is
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Probability from a Collection of Objects - In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option out of the following :19Assertion (A) : The probability that a leap year has 53 Sundays is . Reason (R) : The probability that a non-leap year has 53 Sundays is .
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Theoretical Probability and Elementary Events - 24If a fair coin is tossed twice, find the probability of getting 'atmost one head'.Probability with Cards, Dice and Coins
- 25A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random from the bag. Find the probability that drawn ball is (i) red (ii) yellow.Probability from a Collection of Objects
- A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'. Based on the above, answer the following questions :37 (i)List all possible outcomes of the game.Theoretical Probability and Elementary Events
- A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'. Based on the above, answer the following questions :37 (ii)Find the probability of 'Making Purple'.Theoretical Probability and Elementary Events
- A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'. Based on the above, answer the following questions :37 (iii) (a)For each win, a participant gets ₹ 10, but if he/she loses, he/she has to pay ₹ 5 to the school. If 99 participants played, calculate how much fund could the school have collected.Theoretical Probability and Elementary Events
- A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'. Based on the above, answer the following questions :37 (iii) (b)If the same amount of ₹ 5 has been decided for winning or losing the game, then how much fund had been collected by school ? (Number of participants = 99)Theoretical Probability and Elementary Events
- “Eight Ball” is a game played on a pool table with 15 balls numbered 1 to 15 and a “cue ball” that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15. The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random. Based on the above information, answer the following questions :38 (i)What is the probability that the drawn ball bears number 8 ?Probability from a Collection of Objects
- Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.One school is chosen at random. Then :
Number of Computers Number of Schools 1 – 10 250 11 – 20 200 21 – 50 290 51 – 100 180 101 and more 80 38 (i)Find the probability that the school chosen at random has more than 100 computers.Probability from a Collection of Objects - “Eight Ball” is a game played on a pool table with 15 balls numbered 1 to 15 and a “cue ball” that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15. The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random. Based on the above information, answer the following questions :38 (ii) (a)What is the probability that the drawn ball bears an even number ?Probability from a Collection of Objects
- Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.One school is chosen at random. Then :
Number of Computers Number of Schools 1 – 10 250 11 – 20 200 21 – 50 290 51 – 100 180 101 and more 80 38 (ii) (a)Find the probability that the school chosen at random has 50 or fewer computers.Probability from a Collection of Objects - “Eight Ball” is a game played on a pool table with 15 balls numbered 1 to 15 and a “cue ball” that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15. The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random. Based on the above information, answer the following questions :38 (ii) (b)What is the probability that the drawn ball bears a number, which is a multiple of 3 ?Probability from a Collection of Objects
- Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.One school is chosen at random. Then :
Number of Computers Number of Schools 1 – 10 250 11 – 20 200 21 – 50 290 51 – 100 180 101 and more 80 38 (ii) (b)Find the probability that the school chosen at random has no more than 20 computers.Probability from a Collection of Objects - Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.One school is chosen at random. Then :
Number of Computers Number of Schools 1 – 10 250 11 – 20 200 21 – 50 290 51 – 100 180 101 and more 80 38 (iii)Find the probability that the school chosen at random has 10 or less than 10 computers.Probability from a Collection of Objects - “Eight Ball” is a game played on a pool table with 15 balls numbered 1 to 15 and a “cue ball” that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15. The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random. Based on the above information, answer the following questions :38 (iii)What is the probability that the drawn ball is a solid coloured and bears an even number ?Probability from a Collection of Objects
The 10 board questions to practise first
The questions the board asked again come first, most asked first. Each one says how often and when.
Question 1
Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)
29Two different coins are tossed simultaneously. What is the probability of getting : (i) at least one head ? (ii) at most one tail ? (iii) a head and a tail ?Question 2
Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)
9Three coins are tossed together. The probability of getting exactly one head, is :Tap an option to check your answer.
Question 3
Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year)
4For an event E, , then the value of is :Tap an option to check your answer.
Question 4
Asked 3 times: 2023*, 2024*, 2026 (* = numbers or wording changed that year)
10Which of the following can not be the probability of an event ?Tap an option to check your answer.
Question 5
Asked 3 times: 2023*, 2025*, 2026 (* = numbers or wording changed that year)
31Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.Question 6
Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)
16Meena calculates that the probability of her winning the first prize in a lottery is 0.08. If total 800 tickets were sold, the number of tickets bought by her, isTap an option to check your answer.
Question 7
Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)
Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.19Assertion (A) : The probability that a leap year has 53 Mondays is . Reason (R) : The probability that a non-leap year has 53 Mondays is .Tap an option to check your answer.
Question 8
Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)
31Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that : (i) same number appears on both the dice ? (ii) different number appears on both the dice ?Question 9
Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)
11In a cricket match, a batsman hits the boundary 7 times out of the 42 balls he plays. The probability of his not hitting a boundary is :Tap an option to check your answer.
Question 10
Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)
22The probability of guessing the correct answer of a certain test question is . If the probability of not guessing the correct answer is , then find the value of x.