# Compound Events

A simple event consists of just one outcome, while a compound event consists of two or more simple events. For example, tossing a coin is a simple event, but if we roll a die at the same time, this combination of two simple events counts as a compound event instead.

## How do we find the probability of a compound event?

If we wanted to find the probability of getting an even number when rolling a six-sided die, the probability is simply one-half or

If we want to calculate the probability of a compound event, we have three options:

- Organized lists
- Tree diagrams
- Tables

## Organized lists

When you write an organized list, you simply write out all of the possible outcomes of a compound event. If we rolled a die and flipped a coin, we could write the following list:

1−H, 2−H, 3−H, 4−H, 5−H, 6−H, 1−T, 2−T, 3−T, 4−T, 5−T, and 6−T, where H = heads and T = tails.

If we wanted to find out the probability of rolling heads and either 1, 2, or 3, we would simply find the fraction of the favorable outcome. This is:

## Tree diagrams

We can also create tree diagrams to help us visualize the possibilities.

We start by mapping out the first event:

Then, we add the possibilities of the second event:

If we wanted to flip two coins simultaneously, we might get a tree diagram like this:

## Tables

We can also write out the sample space using tables. This essentially involves turning our organized list into a table with a numbered list of the total events or "rolls" on the left-hand side.

Outcome | Probability |
---|---|

1-H | 1/12 |

2-H | 1/12 |

3-H | 1/12 |

4-H | 1/12 |

5-H | 1/12 |

6-H | 1/12 |

1-T | 1/12 |

2-T | 1/12 |

3-T | 1/12 |

4-T | 1/12 |

5-T | 1/12 |

6-T | 1/12 |

Then, if you were interested in what is the probability of rolling an odd number and a tails, you go to the table and find all the options that fit the condition, 1-T, 3-T, 5-T and then sum the given probabilities,

## Topics related to the Compound Events

Multiplication Rule of Probability

## Flashcards covering the Compound Events

Common Core: High School - Statistics and Probability Flashcards

## Practice tests covering the Compound Events

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

## Get your student the math help they need

Students of all ability levels can benefit from tutoring, whether they''re seeking additional challenges or trying to catch up with compound events or another math topic. Our Educational Directors can create a tutoring plan and schedule that works for your student, so reach out to Varsity Tutors today.

- Actuarial Exam STAM Courses & Classes
- AWS Certified SysOps Administrator Test Prep
- OLSAT Tutors
- Arizona Bar Exam Test Prep
- CCNA Data Center - Cisco Certified Network Associate-Data Center Courses & Classes
- IB Philosophy Tutors
- MAP Tutors
- MLT Exam Courses & Classes
- CLEP Natural Sciences Test Prep
- PARCC Test Prep
- Ruby on Rails Tutors
- Series 24 Courses & Classes
- Vermont Bar Exam Courses & Classes
- 8th Grade Spanish Tutors
- Maryland Bar Exam Courses & Classes
- Actuarial Exam SRM Test Prep
- Film Theory Tutors
- ISEE Courses & Classes
- CCNA Industrial - Cisco Certified Network Associate-Industrial Courses & Classes
- CogAT Test Prep