# Lesson 4: Conditional Probability

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### 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.