Assume that a fair six-sided die is rolled 13 times, and the roll is called a success if the result is in {1,2,3,4}. What is the probability

Question

Assume that a fair six-sided die is rolled 13 times, and the roll is called a success if the result is in {1,2,3,4}. What is the probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls?

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Skylar 3 weeks 2021-09-26T21:46:07+00:00 1 Answer 0

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    2021-09-26T21:47:09+00:00

    Answer:

    The answer to the question is;

    The probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls is \frac{715}{8192}.

    Step-by-step explanation:

    The probability of success = 1/2 =

    probability of failure  = 1/2

    Since we have 4 success we then have 9 failures and the given probability can be solved as ₁₃C₄ × 1/2ⁿ×1/2¹³⁻ⁿ

    Therefore  we have

    ₁₃C₄ × 1/2⁴×1/2⁹ =  715/8192

    That is the probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls = 715/8192.

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