# If the probability that an event will happen is 0.2, what is the probability of the event's complement?

Jan 14, 2018

$P \left(A '\right) = 0.8$

#### Explanation:

If we represent the possibility of the event happening by $A$ then we are given that:

$P \left(A\right) = 0.2$

The complement of this is the probability of the event not happening, which we denote by:

$P \left(\overline{A}\right)$, or $P \left(A '\right)$

There are only two possibilities (the event happens or the event doesn't happen) which lead directly t the complement rule:

$P \left(A\right) + P \left(A '\right) = 1$

Hence:

$P \left(A '\right) = 1 - P \left(A\right) = 1 - 0.2 = 0.8$