Question

If $P\left(E\right)$ and $P\left(\overline{E}\right)$ are the probabilities of two complementary events, then which of the following is always true?

• A. $P\left(E\right)+P\left(\overline{E}\right)=0$
• B. $P\left(E\right)+P\left(\overline{E}\right)=1$
• C. $P\left(E\right)=P\left(\overline{E}\right)$
• D. $P\left(E\right)+P\left(\overline{E}\right)=\frac{1}{2}$

Answer 1

The correct option is B

$P\left(E\right)+P\left(\overline{E}\right)=1$

In a random experiment, the probabilities of all possible events must total to 1, which means some or the other outcome must occur on every trial.
Now, in a complementary event there are only two possible outcomes.
Thus,
$P\left(E\right)+P\left(\overline{E}\right)=1$