# Conditional Probability

How to solve conditional probability problems: formula, examples, and their solutions.

## Formula

P(*B* | *A*) means the probability of (*A* and *B*)

when *A* has already happened.

So P(*B* | *A*) = P(*B* | *A*) / P(*A*).

This is why it is called the 'conditional' probability.

## Example 1

Selecting a gray card (*A*) has already happened.

So this is a conditional probability problem.

So find P(*A*) and P(*A* and *B*).

P(*A*) = 8/15

P(*A* and *B*) = 3/15

P(*B* | *A*) = (3/15) / (8/15) = 3/8.

## Example 2

Sam oversleeping (*A*) has already happened.

So this is a conditional probability problem.

So find P(*A*) and P(*A* and *B*).

P(*A*) = 0.04

P(*A* and *B*) = 0.03

P(*B* | *A*) = 0.03/0.04 = 3/4.