Complement Of An Event

Property A complement of an event is a set of all outcomes of an experiment that are not in a given event. $$ \operatorname{P}(\text{event}) + \operatorname{P}(\text{not event}) = 1 $$.

Examples On a number cube, the probability of rolling a 4 is $\frac{1}{6}$. The probability of not rolling a 4 is $1 \frac{1}{6} = \frac{5}{6}$. In a bag with 4 green and 6 red marbles, the probability of not choosing green is $1 \operatorname{P}(\text{green}) = 1 \frac{4}{10} = \frac{6}{10}$. If the probability of rain is 25% (or 0.25), the probability that it will not rain is $1 0.25 = 0.75$, or 75%.

Explanation The complement is basically 'everything else.' If you want to know the chance of something not happening, this is your go to trick! Instead of counting all the ways an event can fail, just find the probability of it succeeding and subtract that from 1. It’s a clever shortcut for finding the probability of the opposite outcome.