Assume that each born child is equally likely to be a boy or a girl. I

1.	Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl? (ii) atleast one is a girl?
Answer» A family has 2 children, then Sample space = S = {BB, BG,GB,GG}, where B stands for Boy and G for Girl. (i) Let A and B be two event such that A = Both are girls = {GG} B = the youngest is a girl = {BG, GG} Now, P(A/B) = (P(A ∩ B))/P(B) = (1/4)/(2/4) = 1/2 (ii) Let C be event such that C = at least one is a girl = {BG,GB,GG} Now, P(A/C) = (P(A ∩ C))/P(C) = (1/4)/(3/4) = 1/3

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl? (ii) atleast one is a girl?

Answer»

A family has 2 children, then Sample space = S = {BB, BG,GB,GG}, where B stands for Boy and G for Girl.

(i) Let A and B be two event such that

A = Both are girls = {GG}

B = the youngest is a girl = {BG, GG}

Now, P(A/B) = (P(A ∩ B))/P(B) = (1/4)/(2/4) = 1/2

(ii) Let C be event such that

C = at least one is a girl = {BG,GB,GG}

Now, P(A/C) = (P(A ∩ C))/P(C) = (1/4)/(3/4) = 1/3

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Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl? (ii) atleast one is a girl?

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