Complement of an event
Calculate the complement of a probability event in Grade 6 math — subtract the probability from 1 to find the likelihood the event does NOT occur, since all probabilities sum to 1.
Key Concepts
Property The complement of an event is the opposite of the event. The probability of an event and the probability of its complement total 1. $$ P(\text{A}) + P(\text{not A}) = 1 $$.
Examples If $P(\text{rain}) = 0.6$, then the probability of no rain is $1 0.6 = 0.4$. The complement of rolling a number greater than 4 is rolling a number not greater than 4. $P(\text{not 4}) = \frac{4}{6} = \frac{2}{3}$. If $P(\text{winning}) = \frac{1}{10}$, the probability of not winning is $1 \frac{1}{10} = \frac{9}{10}$.
Explanation The complement is the ultimate 'whatever is left.' If the event is 'it rains,' the complement is 'it does not rain.' If the chance of winning is 25%, the complement (not winning) must be the other 75%. They are two sides of the same story and always add up to 1, or 100%. It’s a handy shortcut!
Common Questions
What is the complement of a probability event?
The complement of an event is everything that is NOT that event. If the probability of an event is P, then the probability of its complement is 1 minus P. The event and its complement together account for all outcomes.
How do you calculate the probability of a complement?
Subtract the event probability from 1. For example, if the chance of rain is 0.3, the complement is 1 minus 0.3 equals 0.7, meaning there is a 70 percent chance of no rain.
Why do an event and its complement always add up to 1?
Either the event happens or it does not — there are no other options. So the probabilities of these two outcomes must cover all possibilities and must add up to exactly 1 or 100 percent.
How is understanding complements useful in probability?
Sometimes it is easier to calculate the probability that an event does NOT happen and subtract from 1. This is especially helpful when there are many favorable outcomes but only a few unfavorable ones.