Sum

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

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#### Solution

A family has two children.

∴ Sample space S = {BB, BG, GB, GG}

∴ n(S) = 4

Let event A: At least one of the children is a girl.

∴ A = {GG, GB, BG}

∴ n(A) = 3

∴ P(A) = `("n"("A"))/("n"("S")) = 1/4`

Let event B: Both children are girls.

∴ B = {GG}

∴ n(B) = 1

∴ P(B) = `("n"("B"))/("n"("S")) = 1/4`

Also, A ∩ B = B

∴ P(A ∩ B) = P(B) = `1/4`

∴ Required probability = `"P"("B"/"A")`

= `("P"("B" ∩ "A"))/("P"("A"))`

= `(1/4)/(3/4)`

= `1/3`.

Concept: Independent Events

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