 # 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.

## 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.