roll a die 10 times. find chance of exactly 4 twos?

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  • Alan
    Lv 7
    1 month ago

    Use the binomial probability formula .

    P( exactly k events in n trials) = (n k) p^(k) (1-p)^(n-k)

    where (n k ) = nCk = n! / ( (n-k)! k!)

    n = number of trials

    k = exact number of successes

    p = probability of success in one trial

    so

    P(exactly 4 twos in 10 trials) = ( 10 4) (1/6)^4 (5/6)^6

    P(exactly 4) = (10 4) (5^6/6^10)

    (10 4) = 10! / (6! *4!) = 10*9*8*7 / 4*3*2*1

    (10 4) = 10*9*7/3 = 10*3*7 = 210

    p(exactly 4) = 210 * 5^6/6^10

    P(exactly 4 ) = 3281250 /60466176

    P(exactly 4 ) = 546875 / 10077696

    P(exactly 4 ) = approx. 0.054265876

    so about a 5.43 % chance so not very probable 

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  • Pope
    Lv 7
    1 month ago

    The number of 2s has a binomial distribution.

    p = probability of success on any single trial = 1/6

    n = number of trials = 10

    r = number of successes = 4

    required probability = C(n, r) p^r (1 - p)^(n - r)

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  • 1 month ago

    50/50

    either it happens or it doesn't happen

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