Question

If p(A-B)=1/5,p(A)=1/3,p(B)=1/2,then what is the probability that out of the two events A and B only B would occur?

Answer 1

The probability that out of the two events A and B only B would occur is $\frac{3}{10}$

Explanation

Given that,  $P(A-B)= \frac{1}{5} , P(A)= \frac{1}{3}$ and $P(B)=\frac{1}{2}$

For finding the probability that only B will occur, we need to find  $P(B-A)$

$P(A\cap B)=P(A)-P(A-B)\\ \\ P(A\cap B)= \frac{1}{3}-\frac{1}{5}=\frac{5-3}{15}=\frac{2}{15}$

Now....

$P(B-A)= P(B)-P(A\cap B)\\ \\ P(B-A)=\frac{1}{2}-\frac{1}{5}=\frac{5-2}{10}=\frac{3}{10}$

So, the probability that out of the two events A and B only B would occur is $\frac{3}{10}$