PYQ Vault

Independent events: probability exactly one or a given combination happens

This type of question, asked 7 times: 4 May 2023 S2, 9 May 2023 S2, 16 May 2023 S1, 16 May 2023 S2, 9 May 2024 S2, 22 Apr 2025 S2, 15 May 2026 S2. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    4 May 2023 S2

    140
    A man and his wife appear for an interview for two posts. The probability of the husband's selection is 17\frac{1}{7} and that of the wife's selection is 15\frac{1}{5}. If they appear for the interview independently, then the probability that only one of them is selected, is

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  2. Question 2

    9 May 2023 S2

    122
    Four persons can hit a target correctly with probabilities 12,13,14\frac{1}{2}, \frac{1}{3}, \frac{1}{4} and 15\frac{1}{5} respectively. If all hit at the target independently, then the probability that the target would be hit, is

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  3. Question 3

    16 May 2023 S1

    135
    Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 34,12\frac{3}{4}, \frac{1}{2} and 58\frac{5}{8} respectively, then the probability that the target is hit by P or Q but not by R, is

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  4. Question 4

    16 May 2023 S2

    144
    Two friends A and B apply for a job in the same company. The probabilities of A getting selected is 25\frac{2}{5} and that of B is 47\frac{4}{7}. Then the probability, that one of them is selected, is

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  5. Question 5

    9 May 2024 S2

    142
    A problem in statistics is given to three students A, B and C. Their probabilities of solving the problem are 12,13\frac{1}{2},\frac{1}{3} and 14\frac{1}{4} respectively. If all of them try independently, then the probability that the problem is solved is

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  6. Question 6

    22 Apr 2025 S2

    143
    Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each urn, then the probability that the selection contains 1 black and 2 white balls is

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  7. Question 7

    15 May 2026 S2

    100
    A husband and wife appeared for an interview for two vacancies in an office. The probability of the husband's selection is 15\dfrac{1}{5} and that of the wife's selection is 17\dfrac{1}{7}, then the probability that exactly one of them is selected is...

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