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3 June, 05:39

A coin is flipped 8 times. find the probability of the event: exactly 3 heads

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  1. 3 June, 09:23
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    H, T = 2, Flipped 8 times, Sample space = 2⁸

    Exactly three heads = 3.

    n = 8, r = 3 Probability of success p = (1/2), Probability of failure = (1/2)

    By Binomial Probability distribution

    = ⁿCr * p^r*q^ (n - r)

    ⁸C₃ * (1/2) ³ * (1/2) ⁸ ⁻ ³

    = ⁸C₃ * (1/2) ³ * (1/2) ⁵ ⁸C ₃ = 8*7*6 / (3*2*1) = 56

    = 56 * (1/8) * (1/32)

    = 56/256

    Probability = 56/256
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