Mathematics · Textbook solutions

Probability

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 70 questions

14.1 Probability — A Theoretical Approach

70 q

Solved Examples

Worked · 13

14.1 Eg.1 $Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.$
14.1 Eg.2 $A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the (i) yellow ball? (ii) red ball? (iii) blue ball?$
14.1 Eg.3 $Suppose we throw a die once. (i) What is the probability of getting a number greater than 4? (ii) What is the probability of getting a number less than or equal to 4?$
14.1 Eg.4 $One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will (i) be an ace, (ii) not be an ace.$
14.1 Eg.5 $Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match?$
14.1 Eg.6 $Savita and Hamida are friends. What is the probability that both will have (i) different birthdays? (ii) the same birthday? (ignoring a leap year).$
14.1 Eg.7 $There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?$
14.1 Eg.8 $A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at *random* from the box, what is the probability that it will be (i) white? (ii) blue? (iii) red?$
14.1 Eg.9 $Harpreet tosses two different coins simultaneously (say, one is of ₹1 and other of ₹2). What is the probability that she gets *at least* one head?$
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 $*(Marked in the book "Not from the examination point of view".)* A missing helicopter is reported to have crashed somewhere in the rectangular region shown in Fig. 14.2. What is the probability that it crashed inside the lake shown in the figure? (The rectangular region measures 9 km by 4.5 km; the lake inside it measures 3 km by 2.5 km.)$
14.1 Eg.12 $A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that (i) it is acceptable to Jimmy? (ii) it is acceptable to Sujatha?$
14.1 Eg.13 $Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is (i) 8? (ii) 13? (iii) less than or equal to 12?$

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 Q3 $Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?$
Ex 14.1 Q4 $Which of the following cannot be the probability of an event?$
1. A. $\frac{2}{3}$
2. B. $-1.5$
3. C. $15%$
4. D. $0.7$
Ex 14.1 Q5 $If P(E) = 0.05, what is the probability of 'not E'?$
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out
Ex 14.1 Q6 (i) $an orange flavoured candy?$
Ex 14.1 Q6 (ii) $a lemon flavoured candy?$
Ex 14.1 Q7 $It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?$
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 is
Ex 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 be
Ex 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 coin
Ex 14.1 Q10 (i) $will be a 50 p coin?$
Ex 14.1 Q10 (ii) $will not be a ₹5 coin?$
Ex 14.1 Q11 $Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Fig. 14.4). What is the probability that the fish taken out is a male fish?$
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 at
Ex 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 getting
Ex 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 getting
Ex 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 Q16 $12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.$
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 bears
Ex 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 getting
Ex 14.1 Q19 (i) $A?$
Ex 14.1 Q19 (ii) $D?$
Ex 14.1 Q20 $*(Marked in the book "Not from the examination point of view".)* Suppose you drop a die at random on the rectangular region shown in Fig. 14.6. What is the probability that it will land inside the circle with diameter 1 m? (The rectangular region measures 3 m by 2 m.)$
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 that
Ex 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) $\frac{1}{36}$
Ex 14.1 Q22 (ii) $\frac{1}{11}$
Ex 14.1 Q23 $A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.$
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) $\frac{1}{3}$
Ex 14.1 Q25 (ii) $\frac{1}{2}$