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 al 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 born in March

Explanation / Answer

a) P(both are girls) = 0.5x0.5

= 0.25

b) P(both are girls | at least one is a girl) = P(both are girls)/P(at least one is a girl)

= 0.25/[1 - P(both are girls)]

= 0.25/(1-0.25)

= 0.3333

c) P(both are girls | at least one is a girl) = 0.3333

This is because month of birth is independent of the gender

d) P(both are girls | elder child is a girl who was born in March) = P(second child is a girl)

= 0.5

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