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

How to find the probability of (*A* or *B*, union): meaning, formula, examples, and their solutions.

## Meaning

P(*A* or *B*) means

the probability of

either event *A* or event *B* happening.

So, to find P(*A* or *B*),

find n(*S*),

total number of ways,

find n(*A* or *B*),

the number of ways

of either *A* or *B* happening,

then find P(*A* or *B*):

P(*A* or *B*) = n(*A* or *B*) / n(*S*).

Probability

## Example 1

Numbers from 1 to 10 are given.

So there are 10 numbers

that can be picked.

So n(*S*) = 10.

Set the event *A* as

picking an even number.

The even numbers from 1 to 10 are

{2, 4, 6, 8, 10}.

And set the event *B* as

picking a prime number.

The prime numbers from 1 to 10 are

{2, 3, 5, 7}.

The numbers that are in either *A* or *B* are

{2, 3, 4, 5, 6, 7, 8, 10}.

So [*A* or *B*] is

{2, 3, 4, 5, 6, 7, 8, 10}.

[*A* or *B*] is {2, 3, 4, 5, 6, 7, 8, 10}.

So n(*A* or *B*) = 8.

n(*S*) = 10

n(*A* or *B*) = 8

So P(*A* or *B*) = 8/10.

Probability

Divide the numerator and the denominator by 2.

Then 4/5 is the answer.

## Formula

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

When you add P(*A*) and P(*B*),

P(*A* and *B*) [green] is counted twice.

So P(*A* and *B*) is subtracted.

This formula is used

when both P(*A* or *B*) and P(*A* and *B*) are used together.

Probability of (*A* and *B*, Intersection)

## Example 2

Write the given probabilities.

P(*A*) = 0.6

P(*B*) = 0.7

P(*A* and *B*) = 0.4

P(*A*) = 0.6

P(*B*) = 0.7

P(*A* and *B*) = 0.4

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

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

## Example 3

Write the given probabilities.

P(*A*) = 0.5

P(*B*) is the one you want to find.

So set P(*B*) = *x*.

P(*A* and *B*) = 0.1

P(*A* or *B*) = 0.8

P(*A*) = 0.5

P(*B*) = *x*

P(*A* and *B*) = 0.1

P(*A* or *B*) = 0.8

So 0.5 + *x* - 0.1 = 0.8.

Solve the given equation.

Then *x* = 0.2.

So P(*B*) = 0.2.