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Geometry

The number of possible outcomes for a compound event using a tree diagram or the fundamental counting principle is determined.

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After completing this tutorial, you will be able to complete the following:

- Determine the number of possible outcomes for a compound event by using a tree diagram.
- Determine the number of possible outcomes for a compound event by using the Fundamental Counting Principle.

A tree diagram is a visual display of all possible outcomes in a compound event.

The following is an example of a tree diagram for the possible outcomes of flipping a coin twice.

Possible outcomes would be as follows {heads, heads}, {heads, tails}, {tails, heads}, {tails, tails} which equal to 4 possible outcomes for the event of flipping a coin twice.

A tree diagram is an excellent way to visually introduce possible outcomes to students; students can see how each combination is found by following the "branches" of the tree diagram. However, as the outcomes become more complex another way to find a solution is needed.

Using the Fundamental Counting Principle is the ideal method to use when finding possible outcomes when there are a large amount of combinations.

The Fundamental Counting Principle states that if an event has m possible outcomes and another independent event has n possible outcomes, then there are m × n possible outcomes for the two events together.

An example of using the Fundamental Counting Principle is provided below.

Event:

Sandy is deciding what uniform to wear tomorrow. She has a blue, pink, and white shirt. She has blue and beige pants and black or brown sneakers. What are all the possible combinations?

Because she has 3 shirts, 2 pants, and 2 sneakers we can multiply these numbers together to find the amount of possible outcomes for this event.

3 × 2 × 2 = 12 possible outcome.

The following key vocabulary terms will be used throughout this Activity Object:

- Fundamental Counting Principle ¬- if an event has m possible outcomes and another independent event has n possible outcomes, then there are m × n possible outcomes for the two events together
- multiplication - a mathematical operation where a number is added to itself for a determined amount of times (i.e. 4 + 4 + 4 + 4 + 4 = 4 × 5 = 20)
- outcomes - the result of an event or experiment.
- tree diagram - a visual map that lists all possible outcomes or choices.

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should know how to multiply whole numbers, and be able to recognize a tree diagram. |

Course | Geometry |

Type of Tutorial | Concept Development |

Key Vocabulary | counting outcomes, counting principles, probability |