A family has exactly two children. Assume that the probability of having a girl

Question

A family has exactly two children. Assume that the probability of having a girl is equal to that of having a boy a) Indicate the sample space. b) Indicate the subsets of the sample space corresponding to the following events: A: both children are girls B: at least one of the children is a girl C: the elder child is a girl c) Find the probability that both children are girls d) Find the probability that both children are girls given that at least one of them is a girl. e) Find the probability that the elder child is a boy, given that the family has at least one girl.

Explanation / Answer

let girl Child is represent by G and boy with B

a) therefore sample space ={BB ; BG ; GB ; GG}

b) A ={GG}

B ={ BG ;GB ;GG}

C ={ GB ; GG}

c) probability =P(first child is girl and second child is girl) =(1/2)*(!/2) =1/4

d) probability =P(both are girls and at least one girl)/P(at least one is girl) =(1/4)/(3/4) =1/3

e)probability =P(elder child is a boy and family has at least one girl)/P(at least one girl) =(1/4)/(3/4) =1/3

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