The probabilities of four cricketers A, B, C and D scoring more than 50 runs in a match are 12,13,14 and110 . It is known that exactly two of the players scored more than 50 runs in a particular match. The probability that these players were A and B is

Let E1 be the event that exactly two players scored more than 50 runs then P(E1)=12×13×34×910 +12×23×14×910+12×23×34×110+12×13×14×910 +12×23×34×110+12×23×14×110=65240 Let E2 be the event A and B scored more than 50 runs, then P(E1∩E2)=12×13×34×910=27240 ∴ desired probability = P(E2/E1)=P(E1∩E2)P(E1)=2765