What is the probability of a complement of an event?

The complement of an event is the probability of that event not occurring. It is denoted by P(A').

To find the probability of the complement of an event, we subtract the probability of the event from 1. That is, P(A') = 1 - P(A).

For example, if the probability of event A occurring is 0.3, then the probability of its complement, A' not occurring, is 0.7. This can be calculated as follows:

P(A') = 1 - P(A)
P(A') = 1 - 0.3
P(A') = 0.7

The complement rule can be used to find the probability of an event indirectly. For example, if we want to find the probability of event A, but it is easier to find the probability of its complement, A', we can use the complement rule to find P(A).

For instance, if the probability of A' not occurring is 0.6, then the probability of A occurring is 0.4. This can be calculated as follows:

P(A) = 1 - P(A')
P(A) = 1 - 0.6
P(A) = 0.4

In summary, the probability of the complement of an event is found by subtracting the probability of the event from 1. The complement rule can also be used to find the probability of an event indirectly.