Question

If A, B are two independent events, $P\left(A\right)=\frac{3}{4}$ and $P\left(B\right)=\frac{5}{8}$ , then $P(A\cup B)=$

• A. $\frac{3}{32}$
• B. $\frac{29}{32}$
• C. $\frac{15}{32}$
• D. $\frac{5}{32}$

Answer 1

The correct option is B $\frac{29}{32}$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
A, B are two independent events so $P(A\cap B)=P\left(A\right)P\left(B\right)$
$P(A\cup B)=\frac{3}{4}+\frac{5}{8}-(\frac{3}{4}\times \frac{5}{8})$

$P(A\cup B)=\frac{29}{32}$