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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.

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

1/2

, since half of the numbers are even. If we want to calculate the probability of a compound event, we have three options:

- Organized lists
- Tree diagrams
- Tables

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:

3/12

or 1/4.

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:

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,

1/12 + 1/12 + 1/12 = 3/12 or 1/4th

Multiplication Rule of Probability

Common Core: High School - Statistics and Probability Flashcards

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

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.

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