# Conditional Probability Formula

Conditional Probability is a measure of the probability of an event given that another event has occurred.

If the event of interest is A and the event B is known or assumed to have occurred, “the conditional probability of A given B”, or “the probability of A under the condition B”, is usually written as P(A|B), or sometimes PB(A).

When B is given by A, then conditional probability is,

\[\LARGE P(B|A)= \frac{P(A\cap B)}{P(A)}\]

When A is given by B, then the conditional probability is

\[\LARGE P(A|B)= \frac{P(A\cap B)}{P(B)}\]

### Solved Examples

**Question 1:**

**Solution:**