# A family has two children. Find the probability that both the children are girls, given that atleast one of them is a girl - Mathematics and Statistics

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

#### 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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