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Geometry

Compound independent events to compare probabilities in order to determine fairness in a game are used.

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

- Determine if an event is more likely or equally likely to occur.
- Design a probability experiment to test predictions about fairness related to the probabilities for the sum of two dice.

The likelihood line demonstrates the continuum of probability that an event will occur.

Since probability is a ratio, the probability of any event can be plotted on a number line from 0 to 1.

The event, which falls on the far left side of the likelihood line is the least likely to occur because it has a probability closest to zero. If an event falls on the far right side of the likelihood line, it has a probability of very close to one whole. Events falling in the center of the line have about a fifty percent chance of occurring.

Likelihood lines are typically used in early probability instruction to provide a quick overview of how likely an event can occur. Students can generate a list of real-life events and plot them on the likelihood line.

In this Activity Object, students will create a game using the outcomes of rolling two dice in such a way that one pawn is more likely to win or both are equally likely to win.

Theoretical probability is calculated by dividing the number of outcomes for a specific event by the number of total events possible.

For example, when flipping a penny, the penny could land on either heads or tails resulting in two possible outcomes. To determine the probability of the penny landing on heads:

In this Activity Object, the term theoretical is not used directly; however, since the probability of the sum of two dice is not tested in an actual experiment, it is important for students to know that all of the probabilities discussed in this Activity Object are theoretical. At the end of the Activity Object, students are given the opportunity to play the game. The results of the game represent the experimental probability, the probability of the event actually occurring.

Theoretical probability for the sum of two dice.

A simple chart can be used to list the outcomes of the sum of two dice.

Using this chart, you can easily see that two dice with the sum of 7 will occur most often, and two dice with a sum of either 2 or 12 will occur least often.

A game is fair when all players are equally likely to win.

In this Activity Object, students determine if the game they create is fair. In a fair game, the probability of each player winning must match. For example, we would determine the fairness of the game below by finding the probability of each player winning.

Player 1 has one out of two chances of landing on red. The theoretical probability of landing on red when spinning ten times is 5 out of 10. Player 2 has one out of five chances of landing on red. The theoretical probability of landing on red when spinning ten times is 2 out of 10. Therefore, this game is unfair because player one and player two do not have an equally likely chance of winning the game.

Approximate Time | 15 Minutes |

Pre-requisite Concepts | Students should know the concept of probability. |

Course | Geometry |

Type of Tutorial | Concept Development |

Key Vocabulary | probability, more likely, equally likely |