Probability of (not A, Complement)

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.

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. If you randomly pick a number, find P(not multiples of 3).

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.