1.

A die isrolled. If the outcome is an odd number, what is the probability that it isprime?

Answer» When a die is rolled, the sample space is given by
`S={1, 2, 3, 4, 5 6}`.
Let A = event of getting a prime number, and
B = event of getting and odd number.
Then, `A={2, 3, 5}, B={1, 3, 5}` and `A nn B={3, 5}`.
`:. P(A)=(n(A))/(n(S))=3/6 =1/2, P(B)=(n(B))/(n(S))=3/6=1/2`
and `P(A nn B)=(n (Ann B))/(n(S))=2/6=1/3`.
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))=((1//3))/((1//2))=(1/3xx2/1)=2/3`
`P(A//B)=(P(A nn B))/(P(B))=((1//3))/((1//2))=(1/3xx2/1)=2/3`
Hence, the required probability is `2/3`.


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