The probability that at least one of the events A and B occurs is 35. If A and B occur simultaneously with probability 15, then P(A)+P(B) is

A
2/5
B
4/5
C
6/5
D
7/5

Solution:

Here,

$P (A \cup B) = \frac{3}{5} and P (A \cap B) = \frac{1}{5}$

So, from the addition theorem,

$\begin{array}{l} \frac{3}{5} = P (A) + P (B) - \frac{1}{5} \\ or \frac{4}{5} = 1 - P (\bar{A}) + 1 - P (\bar{B}) \\ ∴ P (A) + P (B) = 2 - \frac{4}{5} = \frac{6}{5} \end{array}$

The probability that at least one of the events A and B occurs is $\frac{3}{5}$ . If A and B occur simultaneously with probability $\frac{1}{5}$ , then $P (A) + P (B)$ is

Solution:

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