# Ten cards numbered 1 through 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?

Ten cards are numbered, hence the sample space is

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, n(S) = 10

Let event A be the even number card drawn, then

A = {2, 4, 6, 8, 10}, n(A)=5

Now probability that an even card is drawn is

Let event B be the cards greater than 3, then

B = {4, 5, 6, 7, 8, 9, 10}, n(B) = 7

So the probability of AB

So, AB = {4, 6, 8, 10}, n(AB)=4

So the required probability will become

Hence the probability that an even card is drawn out of cards that are more than 3 is

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