A couple has two children. Find the probability that both the children are (i) males, if it si known that at least one of the children is male. (ii) females, if it is known that the elder child is a female.

Answer

N/a

Explanation

Sample space is `S={"bb,bg,gb,gg"}`
Here, the boy is represented by b and the girl is represented by g and the first letter represents the elder child and the second letter represents the younger child.
`:.n(S)=4`
(i) Let `E` is event that both children are boys and `F` is the event that at least one child is a boy.
`:.E={"bb"},F={"bg,gb,bb"}impliesn(F)=3`
and `EnnF={"bb"}impliesn(EnnF)=1`
Required Probability
`=P(E/F)=(P(EnnF))/(P(F))=(1//4)/(3//4)=1/3`
(ii) Let `E` is event that both children are girls afnd F is the event the elder child is girl.
`:.E={"gg"},F={gb,gg}` and `EnnF={gg}=E`
`impliesn(E)=1,n(F)=2`
Required Probability
`=P(E/F)=(P(EnnF))/(P(F))=(P(E))/(P(F))=(1//4)/(2//4)=1/2`