November 11, 2016

In this activity, students roll a die that will advance either a blue or red car in a race to the finish. Students can adjust which numbers on the die make each car move, changing the probability that each car will win. This activity allows students to explore experimental and theoretical probability by running multiple races at once and examining how often each car wins and comparing that to how often each car is expected to win. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

- Mathematics > General

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Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.

(+) Use permutations and combinations to compute probabilities of compound events and solve problems.

(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).