Question

If E and $\overline{E}$ denote the happening and not happening of an event and $P\left(\overline{E}\right)=\frac{1}{5},P\left(E\right)=$

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

Answer 1

Answer: (D)

$\frac{4}{5}$

We note that $P$(Event $E$ will occur) + $P$(Event $E$ will not occur) = 1
So, $P\left(E\right)+P\left(\overline{E}\right)=1$
here we are given that $P\left(\overline{E}\right)=\frac{1}{5}$
so, $P\left(E\right)$ = $\frac{4}{5}$
So, $D$ is the correct answer.