Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

4/7

Let  A be the event ' the number on the card drawn is even' and B be the event 'the number on the card drawn is greater than 3' . We have to find P(AIB).

Now, the sample space of the experiment is S = {1,2,3,4,5,6,7,8,9,10}

Then A = {2,4,6,8,10}, B= {4,5,6,7,8,9,10}

and A∩B = {4,6,8,10}

Also   P(A) = 5/10, P(B) = 7/10 and P(A∩B) = 4/10

Then P(AIB) = P(A∩B)/ P(B)

                  = (4/10)/(7/10)

                  = 4/7