Question

Let A and B be two events. Suppose $P\left(A\right)=0.4,P\left(B\right)=p$, and $P(A\cup B)=0.7$. The value of $p$ for which A and B are independent is

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{1}{2}$

Given, $P\left(A\right)=0.4,P\left(B\right)=p$, and $P\left(AUB\right)=0.7$
A and B are independent events.
$\Rightarrow P\left(AUB\right)=P\left(A\right)+P\left(B\right)-P\left(A\right)\times P\left(B\right)$
$0.7=0.4+p-0.4p$
$p=\frac{1}{2}$