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Question
Solve the following:
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that both the children are girls
Solution
A family has two children.
∴ Sample space S = {BB, BG, GB, GG}
A: First child is a girl.
∴ A = {GB, GG}
∴ P(A) = `2/4 = 1/2`
B: Second child is a girl.
∴ B = {BG, GG}
∴ A ∩ B = {GG}
∴ P(A ∩ B) = `1/4`
Required probability = `"P"("B"/"A")`
= `("P"("A" ∩ "B"))/("P"("A"))`
= `(1/4)/(1/2)`
= `1/2`.
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