Question

Ten cards numbered1 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.

Answer 1

Clearly, the sample space is `S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}`.
Let `A =` event that the number on the drawn card is even, and `B=` event that the number on the drawn card is more than 3.
then `A={2, 4, 6, 8, 10}, B={4, 5, 6, 7, 8, 9, 10}`
and `A nn B={4, 6, 8, 10}`.
`:. P(A)=(n(A))/(n(S))=5/10=1/2, P(B)=(n(B))/(n(S))=7/10` and
`P(A nn B)=(n (A nn B))/(n(S))=4/10=2/5`.
Suppose B has already occurred and then A occurs.
So, we have to find `P(A//B)`.
Now, `P(A//B)=(P(A nn B))/(P(B))=((2//5))/((7//10))=(2/5xx10/7)=4/7`.
Hence, the required probability is `4/7`.