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Question
A couple has two children, Find the probability that both children are males, if it is known that at least one of the children is male.
Solution
Let the events of having a boy and having a girl be A and B respectively, and denote them by B and G,
Then event A = both children are boys = {B, B}
B = at least one of the two children is a boy
= {BG, GB, BB}
∴ A ∩ B = {BB}
P(A ∩ B) = `1/4`
and P(B) = `3/4`
∴ `P(A|B) = (P(A ∩ B))/(P(B))`
= `1/4 ÷ 3/4`
= `1/3`
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