Algebra · Textbook solutions

Probability

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 69 questions

Practice set 5.1

4 q
  1. How many possibilities are there in each of the following?
    Ex 5.1 Q.1 (1)
    Vanita knows the following sites in Maharashtra. She is planning to visit one of them in her summer vacation. Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli, Raigad, Matheran, Anandavan.
  2. Ex 5.1 Q.1 (2)
    Any day of a week is to be selected randomly.
  3. Ex 5.1 Q.1 (3)
    Select one card from the pack of 52 cards.
  4. Ex 5.1 Q.1 (4)
    One number from 10 to 20 is written on each card. Select one card randomly.

Practice set 5.2

5 q
  1. For each of the following experiments write sample space 'S' and number of sample points n(S).
    Ex 5.2 Q.1 (1)
    One coin and one die are thrown simultaneously.
  2. Ex 5.2 Q.1 (2)
    Two digit numbers are formed using digits 2, 3 and 5 without repeating a digit.
  3. Ex 5.2 Q.2
    The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop. [Figure: the disc is divided into six sectors, labelled clockwise from the top — Red, Orange, Yellow, Blue, Green, Purple.]
  4. Ex 5.2 Q.3
    In the month of March 2019, find the days on which the date is a multiple of 5. (see the given page of the calender) MARCH - 2019
    MTWTFSS
    123
    45678910
    11121314151617
    18192021222324
    25262728293031
  5. Ex 5.2 Q.4
    Form a 'Road safety commitee' of two, from 2 boys (B1B_1, B2B_2) and 2 girls (G1G_1, G2G_2). Complete the following activity to write the sample space. (a) Committee of 2 boys = □\square (b) Committee of 2 girls = □\square (c) Committee of one boy and one girl = B1G1B_1G_1, □\square, □\square, □\square ∴\therefore Sample space = {..., ..., ..., ..., ..., ...}

Event

4 q

Solved Examples

Worked · 4
  1. Event SolvedEx.1
    Two coins are tossed simultaneously. Write the sample space (S) and number of sample points n(S). Also write the following events in the set form and write the number of sample points in each event. (i) Condition for event A : to get at least one tail. (ii) Condition for event B : to get only one head. (iii) Condition for event C : to get at most one tail. (iv) Condition for event D : to get no head.
  2. Event SolvedEx.2
    A bag contains 50 cards. Each card bears only one number from 1 to 50. One card is drawn at random from the bag. Write the sample space. Also write the events A, B and find the number of sample points in them. (i) Condition for event A : the number on the card is divisible by 6. (ii) Condition for event B : the number on the card is a complete square.
  3. Event SolvedEx.3
    A sanitation committee of 2 members is to be formed from 3 boys and 2 girls. Write sample space 'S' and number of sample points n(S). Also write the following events in set form and number of sample points in the event. (i) Condition for event A : at least one girl must be a member of the committee. (ii) Condition for event B : Committee must be of one boy and one girl. (iii) Condition for event C : Committee must be of boys only. (iv) Condition for event D : At the most one girl should be a member of the committee.
  4. Event SolvedEx.4
    Two dice are rolled, write the sample space 'S' and number of sample points n(S). Also write events and number of sample points in the event according to the given condition. (i) Sum of the digits on upper face is a prime number. (ii) Sum of the digits on the upper face is multiple of 5. (iii) Sum of the digits on the upper face is 25. (iv) Digit on the upper face of the first die is less than the digit on the second die.

Practice set 5.3

6 q
  1. Write sample space 'S' and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).
    Ex 5.3 Q.1 (1)
    One die is rolled, Event A : Even number on the upper face. Event B : Odd number on the upper face. Event C : Prime number on the upper face.
  2. Ex 5.3 Q.1 (2)
    Two dice are rolled simultaneously, Event A : The sum of the digits on upper faces is a multiple of 6. Event B : The sum of the digits on the upper faces is minimum 10. Event C : The same digit on both the upper faces.
  3. Ex 5.3 Q.1 (3)
    Three coins are tossed simultaneously. Condition for event A : To get at least two heads. Condition for event B : To get no head. Condition for event C : To get head on the second coin.
  4. Ex 5.3 Q.1 (4)
    Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits. Condition for event A : The number formed is even Condition for event B : The number formed is divisible by 3. Condition for event C : The number formed is greater than 50.
  5. Ex 5.3 Q.1 (5)
    From three men and two women, environment committee of two persons is to be formed. Condition for event A : There must be at least one woman member. Condition for event B : One man, one woman committee to be formed. Condition for event C : There should not be a woman member.
  6. Ex 5.3 Q.1 (6)
    One coin and one die are thrown simultaneously. Condition for event A : To get head and an odd number. Condition for event B : To get a head or tail and an even number. Condition for event C : Number on the upper face is greater than 7 and tail on the coin.

Probability of an event

4 q

Solved Examples

Worked · 4
  1. Probability of an event SolvedEx.1
    Find the probability of the following, when one coin is tossed. (i) getting head (ii) getting tail
  2. Probability of an event SolvedEx.2
    If one die is rolled then find the probability of each of the following events. (i) Number on the upper face is prime (ii) Number on the upper face is even.
  3. Probability of an event SolvedEx.3
    A card is drawn from a well shuffled pack of 52 playing cards. Find the probability of each event. The card drawn is (i) a red card (ii) a face card
  4. Probability of an event SolvedEx.4
    A box contains 5 strawberry chocolates, 6 coffee chocolates and 2 peppermint chocolates. Find the probability of each of the following events, if one of the chocolates is picked from the box at random. (i) it is a coffee chocolate. (ii) it is a peppermint chocolate.

Practice set 5.4

11 q
  1. If two coins are tossed, find the probability of the following events.
    Ex 5.4 Q.1 (1)
    Getting at least one head.
  2. Ex 5.4 Q.1 (2)
    Getting no head.
  3. If two dice are rolled simultaneously, find the probability of the following events.
    Ex 5.4 Q.2 (1)
    The sum of the digits on the upper faces is at least 10.
  4. Ex 5.4 Q.2 (2)
    The sum of the digits on the upper faces is 33.
  5. Ex 5.4 Q.2 (3)
    The digit on the first die is greater than the digit on second die.
  6. There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn -
    Ex 5.4 Q.3 (1)
    shows an even number.
  7. Ex 5.4 Q.3 (2)
    shows a number which is a multiple of 5.
  8. A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is
    Ex 5.4 Q.4 (1)
    an odd number ?
  9. Ex 5.4 Q.4 (2)
    a multiple of 5 ?
  10. A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is -
    Ex 5.4 Q.5 (1)
    an ace.
  11. Ex 5.4 Q.5 (2)
    a spade.

Problem set 5

35 q
  1. Choose the correct alternative answer for each of the following questions.
    PS5 Q.1 (1)
    Which number cannot represent a probability ?
    1. A.
      23\dfrac{2}{3}
    2. B.
      1.5
    3. C.
      15 %
    4. D.
      0.7
  2. PS5 Q.1 (2)
    A die is rolled. What is the probability that the number appearing on upper face is less than 3 ?
    1. A.
      16\dfrac{1}{6}
    2. B.
      13\dfrac{1}{3}
    3. C.
      12\dfrac{1}{2}
    4. D.
      0
  3. PS5 Q.1 (3)
    What is the probability of the event that a number chosen from 1 to 100 is a prime number ?
    1. A.
      15\dfrac{1}{5}
    2. B.
      625\dfrac{6}{25}
    3. C.
      14\dfrac{1}{4}
    4. D.
      1350\dfrac{13}{50}
  4. PS5 Q.1 (4)
    There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5 ?
    1. A.
      15\dfrac{1}{5}
    2. B.
      35\dfrac{3}{5}
    3. C.
      45\dfrac{4}{5}
    4. D.
      13\dfrac{1}{3}
  5. PS5 Q.1 (5)
    If n(A) = 2, P(A)=15P(A) = \dfrac{1}{5}, then n(S) = ?
    1. A.
      10
    2. B.
      52\dfrac{5}{2}
    3. C.
      25\dfrac{2}{5}
    4. D.
      13\dfrac{1}{3}
  6. PS5 Q.2
    Basketball players John, Vasim, Akash were practising the ball drop in the basket. The probabilities of success for John, Vasim and Akash are 45\dfrac{4}{5}, 0.83 and 58% respectively. Who had the greatest probability of success ?
  7. In a hockey team there are 6 defenders , 4 offenders and 1 goalee. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that -
    PS5 Q.3 (1)
    The goalee will be selected.
  8. PS5 Q.3 (2)
    A defender will be selected.
  9. PS5 Q.4
    Joseph kept 26 cards in a cap, bearing one English alphabet on each card. One card is drawn at random. What is the probability that the card drawn is a vowel card ?
  10. A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,
    PS5 Q.5 (1)
    a red balloon
  11. PS5 Q.5 (2)
    a blue balloon
  12. PS5 Q.5 (3)
    a green balloon.
  13. PS5 Q.6
    A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?
  14. Six faces of a die are as shown below. [Figure: the six faces bear the letters A, B, C, D, E, A.] If the die is rolled once, find the probability of -
    PS5 Q.7 (1)
    'A' appears on upper face.
  15. PS5 Q.7 (2)
    'D' appears on upper face.
  16. A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears
    PS5 Q.8 (1)
    an odd number
  17. PS5 Q.8 (2)
    a complete square number.
  18. PS5 Q.9
    Length and breadth of a rectangular garden are 77 m and 50 m. There is a circular lake in the garden having diameter 14 m. Due to wind, a towel from a terrace on a nearby building fell into the garden. Then find the probability of the event that it fell in the lake.
  19. In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at
    PS5 Q.10 (1)
    8.
  20. PS5 Q.10 (2)
    an odd number.
  21. PS5 Q.10 (3)
    a number greater than 2.
  22. PS5 Q.10 (4)
    a number less than 9.
  23. There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that a card drawn shows,
    PS5 Q.11 (1)
    a natural number.
  24. PS5 Q.11 (2)
    a number less than 1.
  25. PS5 Q.11 (3)
    a whole number.
  26. PS5 Q.11 (4)
    a number is greater than 5.
  27. A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is -
    PS5 Q.12 (1)
    red.
  28. PS5 Q.12 (2)
    not red
  29. PS5 Q.12 (3)
    either red or white.
  30. PS5 Q.13
    Each card bears one letter from the word 'mathematics' The cards are placed on a table upside down. Find the probability that a card drawn bears the letter 'm'.
  31. PS5 Q.14
    Out of 200 students from a school, 135 like Kabbaddi and the remaining students do not like the game. If one student is selected at random from all the students, find the probability that the student selected dosen't like Kabbaddi.
  32. A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a - [Note: marked ★ (challenging) in the textbook.]
    PS5 Q.15 (1)
    prime number
  33. PS5 Q.15 (2)
    multiple of 4
  34. PS5 Q.15 (3)
    multiple of 11.
  35. PS5 Q.16
    The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero. [Note: marked ★ (challenging) in the textbook.]