Question

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

Answer 1

Given ,

Probability of only A = P ( A - B) =
$\frac{1}{5}$

We know that,


$P(A-B) = P(A) - P(A \cup B) \:$

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

In the same way,

P(B) = P(A-B) - $P( A \cup B)$

P(B) = 1/5 - 2/15

P(B) = 3-2/15 = 1/15.

Therefore, The probability of only B would occur is 1/15