# Conditional probability

#### You’re one step closer to a better grade.

Learn with less effort by getting unlimited access, progress tracking and more.

0/1

### Introduction

#### Lessons

1. Definition of Conditional Probability
$\cdot$ P(B | A): probability of event B occurring, given that event A has already occurred.

$\cdot$ recall: P(A and B) = P(A) $\cdot$ P(B | A)
then: P(B | A) = $\frac{P(A\;and \;B)}{P(A)}$
0/3

### Examples

#### Lessons

1. Probability Tree Diagram
Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.
A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;
if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.
1. Find the probability that a red ball is selected.
2. Given that the ball selected is red, find the probability that it came from Bag A.
2. It is known that 60% of graduating students are girls. Two grads are chosen at random. Given that at least one of the two grads are girls, determine the probability that both grads are girls.

## Become a Member to Get More!

• #### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.

• #### Make Use of Our Learning Aids

###### Practice Accuracy

See how well your practice sessions are going over time.

Stay on track with our daily recommendations.

• #### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.

• #### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Basics
$\cdot$ P(B | A): probability of event B occurring, given that event A has already occurred.

$\cdot$ recall: P(A and B) = P(A) $\cdot$ P(B | A)
then: P(B | A) = $\frac{P(A\;and \;B)}{P(A)}$