Question

A family has two children. What is the probability that both the children are girls given that at least one of them is a girl?

Answer 1

Let B denote a boy and G denote a girl.

Then the sample, S = {BG, GB, BB, GG}.

∴ n(S) = 4

Let E be the event that both children are girls.

Let F be the event that at least one of them is a girl.

Then E = {GG}, n(E) = 1

F = {BG, GB, GG}, n(F) = 3

P(F) = `("n"("F"))/("n"("S")) = 3/4`

E ∩ F = {GG}, n(E ∩ F) = 1

P(E ∩ F) = `("n"("E" ∩ "F"))/("n"("S")) = 1/4`

Required Probability `"P"("F"/"E") = ("P" ("E" ∩ "F"))/("P"("F")) = (1/4)/(3/4) = 1/3`