# Chapter 11: Applications of Probability

**At Grade**Created by: CK-12

Here you will learn to calculate probabilities of events, including unions of events and intersections of events. You will also learn about independence and conditional probability, and applications of these concepts in everyday life. You will learn to count large numbers of outcomes using permutations and combinations. Finally, you will use probability to think about fairness as you analyze games and decisions.

- 11.1.
## Descriptions of Events

- 11.2.
## Independent Events

- 11.3.
## Conditional Probability

- 11.4.
## Two-Way Frequency Tables

- 11.5.
## Everyday Examples of Independence and Probability

- 11.6.
## Probability of Unions

- 11.7.
## Probability of Intersections

- 11.8.
## Permutations and Combinations

- 11.9.
## Probability to Analyze Fairness and Decisions

### Chapter Summary

You learned to describe events as well as unions of events, intersections of events, and complements of events. You learned that two events are independent if the result of one event does not change the probability of the other event occurring. You learned two ways to test for independence of events. Two events A and B are independent if:

- \begin{align*}P(A \cap B)=P(A)P(B)\end{align*}
P(A∩B)=P(A)P(B) - \begin{align*}P(A|B)=P(A) \ and \ P(B|A)=P(B)\end{align*}
P(A|B)=P(A) and P(B|A)=P(B)

You learned about conditional probability and its relationship to independence. You also explored some everyday examples of independence and conditional probability.

You learned how to find the probability of unions and intersections. You also learned how to use permutations and combinations to count the outcomes in an event or in a sample space in order to determine a probability.

Finally, you used your knowledge of probability to analyze games, decisions and strategies.

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