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

Answer 1

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`.