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

How to find the probability of (*A* and *B*, intersection): meaning, example and its solution.

## Meaning

P(*A* and *B*) means

the probability of

both events *A* and *B* happening.

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

find n(*S*),

total number of ways,

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

the number of ways

of both *A* and *B* happening,

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

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

Probability

## Example

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 odd number.

The odd numbers from 1 to 10 are

{1, 3, 5, 7, 9}.

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 both *A* and *B* are

{3, 5, 7}.

So [*A* and *B*] is

{3, 5, 7}.

[*A* and *B*] is {3, 5, 7}.

So n(*A* and *B*) = 3.

n(*S*) = 10

n(*A* and *B*) = 3

So P(*A* and *B*) = 3/10.

Probability