Question

If the probability of an event $E$ is $\frac{7}{16}$, then what is the probability of complement of the event $E?$

• A. $\frac{7}{16}$
• B. $\frac{9}{16}$
• C. $\frac{11}{16}$
• D. $\frac{11}{16}$

Answer 1

The correct option is B $\frac{9}{16}$

$\underset{–}{\text{Given}:}$
Probability of an event, $E$ is $\frac{7}{16}$

$\Rightarrow \text{P}\left(E\right)=\frac{7}{16}$

$\underset{–}{\text{Need to Find}:}$
Probability of complement event of the event $E$, i.e., $\text{P}\left(\overline{E}\right)$

As we know that,
$\text{P}\left(E\right)+\text{P}\left(\overline{E}\right)=1$

$\Rightarrow \text{P}\left(\overline{E}\right)=1-P\left(E\right)$

$\Rightarrow \text{P}\left(\overline{E}\right)=1-\frac{7}{16}$ $(\because \text{P}\left(E\right)=\frac{7}{16})$

$\Rightarrow \text{P}\left(\overline{E}\right)=\frac{16}{16}-\frac{7}{16}$

$\Rightarrow \text{P}\left(\overline{E}\right)=\frac{16-7}{16}$

$\Rightarrow \text{P}\left(\overline{E}\right)=\frac{9}{16}$

The probability of complement of the event $E$ $=\text{P}\left(\overline{E}\right)=\frac{9}{16}$

Therefore, option (b.) is the correct choice.