3. Consider a family of two children. Assume that birth month is independent of

Question

3. Consider a family of two children. Assume that birth month is independent of sex, with boys and girls equally likely and all months equally likely. You may also assume that the sex and birth month of one child are independent of the sex and birth month of the other child (a) Find the probability that the children are both girls. (b) Find the probability that the children are both girls given that at least one is a girl. 1 mark] 2 marks] (c) Find the probability that the children are both girls given that at least one is a girl who 3 marks (d) Find the probability that the children are both girls given that the elder child is a girl [3 marks] was born in March. who was bor in March.

Explanation / Answer

Answer :

P(girl) = 0.5

P (boy) = 0.5

A) p(both girls) = 0.5 * 0.5 = 0.25

B) p(both girls| atleast 1 is girl ) = >

P(atleast 1 girl) = 1- p(both boy) = 1-0.5*0.5 = 0.75

P( both girls | atleast 1 girl) = 0.25/0.75 = 1/3

(C). P( child born in March ) = 1/12

P( atleast one girl) = 0.75

P(atleast one girl and girl born in March) = 0.5*1/12*0.5+ 0.5*0.5*1.2 + 2*(0.5*0.5*1/12) + 0.5*1/12*0.5*1/12 = 0.085069

P(both girls | atleast one girl and girl born in March ) = (2*0.5*0.5*1/12)/0.085069 = 0.489795

(D) p(elder girl born in March) = 1/12*0.5( 0.5 + 0.5) = 0.041666

P(both girl | elder sister born in March) =( 0.5*1/12*0.5)/0.041666= 0.5

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