# Lesson 4: Conditional Probability

### Introduction

In this lesson, we'll focus on finding a particular kind of probability called a conditional probability. In short, a conditional probability is a probability of an event given that another event has occurred. For example, rather than being interested in knowing the probability that a randomly selected male has prostate cancer, we might instead be interested in knowing the probability that a randomly selected male has prostate cancer *given that* the male has an elevated prostate-specific antigen. We'll explore several such conditional probabilities.

### Objectives

In this lesson, our goals are to:

- Understand the definition of conditional probability.
- Learn how to use the relative frequency approach to assigning probability to find the conditional probability of an event from a two-way table.
- Learn how to use the formula for conditional probability.
- Learn how to use the multiplication rule to find the probability of the intersection of two events.
- Learn how to use the multiplication rule to find the probability of the intersection of more than two events.
- Learn to apply the techniques learned in the lesson to new problems.