A family has 2 children.The probability that both of them are boys if it is known that one of them is a boy

Options

A. `(1)/(3)`
B. `(2)/(3)`
C. `(3)/(4)`
D. `(1)/(4)`

Answer

A

Explanation

Let `S={(B_(1)B_(2),B_(1)G_(2),G_(1)B_(2),G_(1)G_(2)}`
Let A = event that both are boys and B = event that one of the two is a boy .
Then A `={B_(1),B_(2)} ,B=(B_(1),B_(2),B_(1),G_(1)B_(2)} " and " B={B_(1),B_(2)}`
`:. P(A//B) =(n(A nn B))/(n(B)) =(1)/(3)`