# Probability of (not *A*, Complement)

How to find the probability of (not *A*, complement): formula, example, and its solution.

## Formula

P(not *A*) = 1 - P(*A*)

P(not *A*): Probability of the event *A* not happening

P(*A*): Probability of the event *A* happening

This formula is used

when it's easier to find P(*A*).

## Example

Numbers from 1 to 11 are given.

So there are 11 numbers

that can be picked.

So n(*S*) = 11.

Finding the multiples of 3

is easier than

finding the numbers that are not the multiples of 3.

So set the event *A* as

picking the multiples of 3.

The multiples of 3 from 1 to 11 are

{3, 6, 9}.

So n(*A*) = 3.

n(*S*) = 11

n(*A*) = 3

So P(*A*) = 3/11.

Probability

Your goal is to find P(not *A*):

P(not multiples of 3).

P(*A*) = 3/11

So P(not *A*) = 1 - 3/11.

So 8/11 is the answer.