There are 25 girls and 15 boys in class XI and 30 boys and 20 girls in class XII. If a student chosen from a class, selected at random, happens to be a boy, find the probability that he has been chosen from class XII.

Explanation

Let `E_1`= The student is choosen from class XI.
`E_2` The student is choosen from class XII.
A= The student is a boy.`P(E_1)=P(E_2)=1/2`
`P(A//E_1)=15/40=3/8`
P(A//E_2)=30/50=6/10`
We went to find `P(E_2//A)`. By Baye.s theoren
`P(E_2|A)=(P(E_2)P(A//E_2))/(P(E_1)P(A//E_1)+P(E_2)P(A//E_2))`
`=(1/2cdot 6/10)/(1/2cdot3/8+1/2cdot6/10)=(6/10)/((15+24)/40)=24/39=8/13`