A couple has 2 children. find the probability that the both are boys if it is given that (i) one of the child is boy (ii) the older child is boy.

Explanation

Sample `S ={B_{1} B_{2}, B_{1} G_{2}, G_{1} B_{2}, G_{1} G_{2}}`,


`B_{1}` = older boy and `G_{1}`= girl respectively.


Take `E_{1}=` Both are boys;


`E_{2}=` One is a boys


`E_{3}=` The older a boy


Then, (i) `P(E_{1} / E_{2})=P(frac{E_{1} cap E_{2}}{E_{2}})=frac{frac{1}{3}}{frac{4}{4}}=frac{1}{3}`


(ii)
`P(E_{1} / E_{3})=P(frac{E_{1} cap E_{3}}{E_{3}})=frac{frac{1}{4}}{frac{2}{4}}=frac{1}{2}`