# Probability: Not A

How to find the probability P(not A): formula, 1 example, and its solution.

## Formula

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

P(not A): Probability of A not happening

P(A): Probability of A happening

Use this formula

when finding P(not A)

seems to be easier than

finding P(A).

An event A either happens or not happens.

There are only two cases.

So P(A) + P(not A) = 1.

Move P(A) to the right side.

Then P(not A) = 1 - P(A).

## Example

Solution

Solution (Detail)

Finding the multiple of 3

seems to be easier than

finding the numbers

that are not the multiple of 3.

Set A as

picking a multiple of 3 from 1 to 10.

{3, 6, 9}

The number of {3, 6, 9} is 3.

n(A) = 3

The number of [1 ~ 10] is 10.

n(S) = 10

Then P(A) = 3/10.

Probability

P(A) = 3/10

Then

P(not A) = 1 - 3/10.

1 = 10/10

10/10 - 3/10 = 7/10

So 7/10 is the answer.