PYQ Vault

Independent events: probability that exactly one or at least one happens

This type of question, asked 3 times: 3 Mar 2023 Tier II, 6 Mar 2023 Tier II, 18 Jan 2025 Tier II. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    3 Mar 2023 Tier II

    27
    A speaks the truth 5 out of 7 times and B speaks truth 8 out of 9 times. What is the probability that they contradict each other in stating the same fact?

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  2. Question 2

    6 Mar 2023 Tier II

    8
    The probabilities of solving a problem by three students A, B and C are 37\frac{3}{7}, 59\frac{5}{9} and 15\frac{1}{5}, respectively. The probability that problem will be solved is:

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  3. Question 3

    18 Jan 2025 Tier II

    7
    Let A and B be two players who are playing the game to hit the target. The probabilities of hitting the target by A and B is 23\frac{2}{3} and 34\frac{3}{4}, respectively. What is the probability that exactly one of them hit the target?

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