There are two children in a family. Find the probability that both boys if it is known that:
(i) one of the children is a boy
(ii) Older child is a by

Answer

N/a

Explanation

For two children the sample space
`S={B_(1)B_(2),B_(1)G_(2),G_(1)B_(2),G_(1)G_(2)}`
Where B and G denote for boy and girl respectively and older child comes first.
(i) Let `E=` event that both children are boys
`={B_(1) B_(2)}`
and `F=` event that one child is a boy
`={B_(1)B_(2),B_(1)G_(2),G_(1)B_(2)}`
`:.EnnF={B_(1)B_(2)}`
Now `P(E//F)=(P(EnnF))/(P(F))=(1//4)/(3//4)=1/3`
(ii) Let `H+` event that older child is a boy
`={B_(1)B_(2),B_(1)G_(2)}`
`EnnH={B_(1)B_(2)}`
`P(E//H)=(P(EnnH))/(P(H))=(1//4)/(2//4)=1/2`