# Probability of (*A* or *B*, Union)

How to solve the probability of (A or B, union) problems: formula, examples, and their solutions.

## Formula

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

By P(*A*) + P(*B*),

the intersection P(*A* and *B*) is added twice.

So we subtract P(*A* and *B*).

## Example 1

There are 8 ways to select a gray card.

There are 3 ways to select a circle card.

There's 1 way to select a gray and circle card.

There are 15 ways to select a card.

So the probability is

8/15 + 3/15 - 1/15 = 10/15, 2/3.

## Example 2

Put the given conditions into the formula.

Then P(*A* or *B*) = 0.9.

## Example 3

Set P(*B*) = *x*.

And put this *x* and the given conditions

into the formula.

Then *x* = 0.4.