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Geometry

How the probability of simple compound events using a tree diagram can be determined is explained.

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

- Determine the probability of simple compound events using a tree diagram.

There are several important points that should be shared with learners before beginning this Activity Object.

- We are calculating theoretical probability when using a tree diagram.
Theoretical probability is calculated by dividing the number of outcomes for a specific event by the number of total events possible. For example, a penny lands on heads: the penny could land on either heads or tails so there are two possible outcomes and only one specific event we wish to happen: landing on heads.

In this Activity Object, learners will use a tree diagram to determine the theoretical probability of a specific event related to the gaming machine.

- The gaming machine experiment represents a compound event.
A compound event is an event that is derived from two other events. For example, if we roll two dice, then the event "getting a six on either the first or second die" is a compound event. There are two figures in the gaming machine; each with a variety of possible properties. In this Activity Object, learners choose an event. For example, 'both figures are spotted". Since the event includes more than one figure, the event is compound.

- The two reels in the gaming machine represent independent events.
Events are independent when the outcome of one event does not influence the outcome of a second event. When the outcome of one event affects the outcome of a second event, the events are dependent. In this Activity Object, the result of one reel does not affect the result in the other reel. Therefore, the events are independent.

- A tree diagram is a visual map of all of the possible outcomes in a probability experiment.
When attempting to determine the possible outcomes from an experiment, it is often helpful to draw a diagram, which illustrates how to arrive at the answer. The tree diagram can be used to determine the probability of individual outcomes within the probability experiment.

The probability of any outcome is the number of outcomes for a specific event divided by the product (multiply) of all possibilities along the path that represents that event on the tree diagram.

Example:

Tossing one penny and rolling one die "landing on heads and two" (H = heads, T = tails)

By following the path of the tree diagram, the probability of landing on heads is and the probability of landing on two is . The Fundamental Counting Principle is used to find the number of possible outcomes. It states that if an event has m possible outcomes and another independent event has n possible outcomes, then there are mn possible outcomes for the two events together.

Using The Fundamental Counting Principle, multiply the probability of landing on heads by the probability of landing on two . The probability for the two events occurring together is

Approximate Time | 15 Minutes |

Pre-requisite Concepts | Students should know the definition of the probability of an event and tree diagrams. |

Course | Geometry |

Type of Tutorial | Concept Development |

Key Vocabulary | probability, tree diagram, simple compound events |