A die is rolled . If the outcome is an odd number what is the probability that it is prime ?

Explanation

When a die is rolled, the sample space is
S={1, 2, 3, 4, 5, 6}
Let A = event of getting an odd no. and
B= event of getting a prime no.
Then, `A ={1, 3, 5}, B={2, 3, 5} " and " AcapB = {3, 5}`
`therefore " " P(A)=(n(A))/(n(S))=3/6=1/2`
`P(B)=(n(B))/(n(S))=3/6=1/2`
` and " " P(AcapB)=(n(AcapB))/(n(S))=2/6=1/3`
Suppose A has already occurred and B occurs. Then, we have to find P(B|A)
Now, `P(B|A)=(P(AcapB))/(P(A))=(1/3)/(1/2)=2/3`