Chapter 5.6, Problem 4QE

Program Plan Intro

Conditional probability:

The conditional probability is generally the measure of an event occurring with respect to another event that has occurred.

Consider an event of interest is $A$ and $B$ is the event which is assumed to be happened, and then the conditional probability of $A$ with respect to $B$ is,

$P\left(\frac{A}{B}\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$

Here,

$P\left(A\cap B\right)$ is the probability of both events $A$ and $B$.

$P\left(B\right)$ is the probability of the event $B$.