A family has two children. What is the probability that both the children are boys given that atleast one of them is a boy ?

Explanation

Let `B` represents a boy and `G` represents a girl. Then,

Sample space `(S) = {(B,B),(G,G),(B,G),(G,B)}`

So, Probability of both of children are boys`,P(A_1) = 1/4`

Probability that at least one of them is a boy `,P(A_2) = 3/4`

Here, we have to find `P(A_1/A_2)`.

`=>P(A_1/A_2) = (P(A_1 nn A_2))/(P(A_2))`

Here, `P(A_1 nn A_2) = 1/4`

`=>P(A_1/A_2) = (1/4)/(3/4) = 1/3`

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