Question

$AandB$ are two independent events such that $P(AUB’)$ $=0.8$ and $P\left(A\right)=0.3$, then $P\left(B\right)$is

• A. $\frac{2}{7}$
• B. $\frac{2}{3}$
• C. $\frac{3}{8}$
• D. $\frac{1}{8}$

Answer 1

The correct option is A

$\frac{2}{7}$

Step1. Finding value for $P\left(B^{\text{'}}\right)$

Given $P(AUB’)=0.8$ and $P\left(A\right)=0.3$

$P(AUB’)=P\left(A\right)+P(B’)–P(A\cap B’)$

As $AandB$are independent events,

$\begin{array}{rcl}P(AUB’)& =& P\left(A\right)+P(B’)–P\left(A\right).P(B’)\end{array}$

$\begin{array}{rcl}& \Rightarrow & 0.8=0.3+P(B’)–0.3P(B’)\end{array}$

$\Rightarrow \begin{array}{rcl}& & 0\end{array}\begin{array}{rcl}& & .\end{array}\begin{array}{rcl}& & 5\end{array}\begin{array}{rcl}& & \end{array}\begin{array}{rcl}& =& \end{array}\begin{array}{rcl}& & 0.7P(B’)\end{array}$

$\begin{array}{rcl}\Rightarrow P(B’)& =& \frac{5}{7}\end{array}$

Step 2. Finding the value for$P\left(B\right)$

Since,

$P\left(B\right)=1-P(B’)$

$$\begin{gathered} P\left(B\right)=1-\left(\frac{5}{7}\right) \\ P\left(B\right)=\frac{2}{7} \end{gathered}$$

Hence, Option(A) is correct.