Suppose that the probability of giving birth to a boy and the probabilityof givi

Question

Suppose that the probability of giving birth to a boy and the probabilityof giving bith to a girt are both 0.5, Find the probablity that in a family of six children, the following occurs. (a) All six children are girs (b) There are three girls and three boys (c) The youngest child is a boy (d) The oldest child is a boy (a) The probability is Type an integer or a simpified fraction.) (b) The probability is Type an integer or a simplified fraction.) (c) The probablty is Type an integer or a simplified fraction) (d) The probability isType an integer or a simpified fraction.)

Explanation / Answer

Binomial distribution: P(X) = nCx px qn-x

n = 6

P(girl) = P(boy) = 1/2

a) P(all 6 children are girls) = (1/2)6

= 1/64

b) P(there are three girls and three boys) = 6C3 x (1/2)3 x (1/2)3

= 5/16

c) P(youngest child is a boy) = 1/2

d) P(oldest child is a boy) = 1/2

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