The chances of Srijit getting admitted to colleges A and B are 60% and 40% respectively.Assume that colleges admit students independently of each other.If Srijit is told that he has been admitted to at least one college,what is the probability that he got admitted to college A?

a)3/5

b)15/19

c)10/13

d)5/7

Let E1: denote the event that Srijit gets admission to College A.

Also let E2: denote the event that Srijit gets admission to College B.

Let E: denote that Srjit gets admission to at least one of the colleges.

To find P(E1|E)=P(E1,E)/P(E)

Now, P(E)=P(E1UE2)=P(E1)+P(E2)-P(E1,E2)=0.6+0.4-(0.6*0.4){Since colleges admit independently}=0.76

P(E1,E)=P(Srijit gets admission to college A and also gets admission to at least one of the colleges)=P(E1)=0.6

Hence required probability=0.6/0.76=15/19….b) is the correct option.