Question

$I f, P (A) = \frac{3}{8}; P (B) = \frac{1}{2} and P (A c a p B) = 1 / 4 then P (A c u p B) =$

0
$\frac{5}{8}$
1
4

Answer: $\frac{5}{8}$

Solution :-

We know that $P (A \cup B) = P (A) + P (B) - P (A \cap B)$

Given that, P (A) = \frac{3}{8}; P (B) = \frac{1}{2} and P (A \cap B) = \frac{1}{4}

\begin{aligned} Then, P (A \cup B) & = & P (A) + P (B) - P (A \cap B) \\ = & \frac{3}{8} + \frac{1}{2} - \frac{1}{4} \\ = & \frac{3 + 4 - 2}{8} \\ = & \frac{5}{8} \cdot \end{aligned}

So, correct answer is option-4, $\to \frac{5}{8}$

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