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29 August, 05:32

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. in a random survey of 10 women in this age group, what is the probability that at least eight were married?

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  1. 29 August, 05:41
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    This is a case of binomial distribution. The formula used in calculations for binomial probability is:

    P = nCr p^r (1-p) ^ (n-r)

    Where,

    P = probability

    nCr = combinations of r from n possibilities

    p = success rate = 40% = 0.40

    n = sample size = 10

    1st: Let us calculate for nCr for r = 8 to 10. Formula is:

    nCr = n! / r! (n-r) !

    10C8 = 10! / 8! 2! = 45

    10C9 = 10! / 9! 1! = 10

    10C10 = 10! / 10! 0! = 1

    Calculating for probabilities when r = 8 to 10:

    P (r=8) = 45 * 0.4^8 (0.6) ^2 = 0.0106

    P (r=9) = 10 * 0.4^9 (0.6) ^1 = 0.0016

    P (r=10) = 1 * 0.4^10 (0.6) ^0 = 0.0001

    Total probability that at least 8 were married = 0.0106 + 0.0016 + 0.0001

    Total probability that at least 8 were married = 0.0123
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