Question

If $A$ and $B$ are two independent events such that $P(A\cup B\text{'})=0.8$ and $P\left(A\right)=0.3$. Then, $P\left(B\right)$ is equal to

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

Answer 1

The correct option is A

$\frac{2}{7}$

Explanation for the correct option:

Find the value of $P\left(B\right)$:

Given, $P(A\cup B\text{'})=0.8$, $P\left(A\right)=0.3$

As we know,

$P(A\cup B\text{'})=P\left(A\right)+P(B\text{'})–P\left(A\right)P(B\text{'})$

$\Rightarrow$ $0.8=0.3+P(B\text{'})–0.3P(B\text{'})$

$\Rightarrow$ $0.5=0.7P(B\text{'})$

$\Rightarrow$ $P(B\text{'})=\frac{5}{7}$

$\because$$P\left(B\right)=1-P(B\text{'})$

$\begin{array}{rcl}& =& 1-\frac{5}{7}\\ & =& \frac{(7-5)}{7}\\ & =& \frac{\mathbf{2}}{\mathbf{7}}\end{array}$

Hence, Option ‘A’ is Correct.