Probability: Not A

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

Formula

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

Example

Solution

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.