Probability: A or B

How to find and use the probability P(A or B): formula, 3 examples, and their solutions.

Example 1

Example

Solution

Set A as
picking an odd number from 1 to 10.
{1, 3, 5, 7, 9}

Set B as
picking a prime number from 1 to 10.
{2, 3, 5, 7}

Then [A or B] is,
write the numbers in either A or B,
{1, 2, 3, 5, 7, 9}.

The number of {1, 2, 3, 5, 7, 9} is 6.
n(A or B) = 6

The number of [1 ~ 10] is 10.
n(S) = 10

Then P(A or B) = 6/10.

Probability

6/10 = 3/5

So 3/5 is the answer.

Formula

Formula

P(A or B) = P(A) + P(B) - P(A and B)

If you add P(A) and P(B),
P(A and B) is added twice.
So P(A and B) is subtracted.

Probability: A and B

Example 2

Example

Solution

P(A) = 0.6
P(B) = 0.7
P(A and B) = 0.4

Then
P(A or B) = 0.6 + 0.7 - 0.4.

+0.7 - 0.4 = +0.3

0.6 + 0.3 = 0.9

So P(A or B) = 0.9.

Example 3

Example

Solution

P(A) = 0.5
P(B) is unknown.
P(A and B) = 0.1
P(A or B) = 0.8

Then 0.5 + P(B) - 0.1 = 0.8.

0.5 - 0.1 = +0.4

Move +0.4 to the right side.

Then P(B) = 0.4.

So 0.4 is the answer.