Textbook Problem

If A and B are any events in a sample space S and $P\left(A\right)\ne 0$ , then the conditional probability of B given A, denoted $P\left(B|A\right)$, equals .

To determine

The appropriate solution for the given fill in the blanks.

Answer to Problem 1TY

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

Explanation of Solution

Given information:

Sample space $S$ and two events $A,B$ such that $P\left(A\right)\ne 0$.

Calculation:

From the conditional probability formula, $P\left(B|A\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)}$ where $P\left(A\right)\ne 0$.

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