PYQ Vault

Probability of exactly r successes in n binomial trials

This type of question, asked 10 times: May 2021 S1, 11 May 2023 S1, 22 Apr 2025 S2, 25 Apr 2025 S1, 25 Apr 2025 S2, 26 Apr 2025 S1, 15 Apr 2026 S1, 20 Apr 2026 S2, 13 May 2026 S2, 15 May 2026 S2. All 10 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    May 2021 S1

    146
    A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective is

    Tap an option to check your answer.

  2. Question 2

    11 May 2023 S1

    149
    The probability that a person who undergoes a bypass surgery will recover is 0.6. The probability that of the six patients who undergo similar operations, half of them will recover is

    Tap an option to check your answer.

  3. Question 3

    22 Apr 2025 S2

    145
    In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

    Tap an option to check your answer.

  4. Question 4

    25 Apr 2025 S1

    135
    A pair of fair dice is thrown 4 times. If getting the same number on both dice is considered as a success, then the probability of two successes are

    Tap an option to check your answer.

  5. Question 5

    25 Apr 2025 S2

    112
    The probability that a student is not a swimmer is 15\frac{1}{5}. The probability that out of 5 students selected at random 4 are swimmers is

    Tap an option to check your answer.

  6. Question 6

    26 Apr 2025 S1

    102
    The probability that a person is not a sportsperson is 16\frac{1}{6}. Then the probability that out of the 6 members of the family, 5 are sportspersons is

    Tap an option to check your answer.

  7. Question 7

    15 Apr 2026 S1

    98
    The centers for disease control have determined that when a person is given a vaccine, the probability that the person will develop immunity to a virus is 0.80.8. If 88 people are given this vaccine, then the probability that exactly 44 will develop immunity is...

    Tap an option to check your answer.

  8. Question 8

    20 Apr 2026 S2

    98
    Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........

    Tap an option to check your answer.

  9. Question 9

    13 May 2026 S2

    98
    Suppose that 60%60\% of all families own a mobile set. If 1111 families are interviewed at random, then the probability that 88 families own a mobile set is..... (Given that (0.6)8=0.0168(0.6)^8 = 0.0168)

    Tap an option to check your answer.

  10. Question 10

    15 May 2026 S2

    98
    It is known that 10%10\% of certain articles manufactured are defective. What is the probability that in a random sample of 1212 such articles, 99 are defective?

    Tap an option to check your answer.