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16 July, 11:50

If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of getting at least 1 correct? if a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by guessing?

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  1. 16 July, 14:00
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    There is a 1/5 chance of getting each question correct. The probability of getting at least 1 correct is written as such:

    P (X ≥ 1) = 1 - P (X = 0)

    This is because the only other option than getting at least one correct is to get nothing correct.

    Since there is a 1/5 chance of getting each question correct, there is a 4/5 chance of getting each question wrong:

    1 - P (X = 0) = 1 - (4/5) ^10 (since there are 10 questions, with a 4/5 chance of missing each one)

    = 1 - 0.1073741824 ≈ 0.8926 = 89.26% chance of getting at least one question correct. Given this probability, it is reasonable to expect to pass by guessing.
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