Lesson Plan

Develop a theoretical probability distribution for a discrete random variable when the outcome probabilities can be computed from a model

Use the multiplication rule for independent events and counting (combinations) to find P(X = k) for each value

Verify the developed distribution sums to 1 and graph it as a probability histogram

Compute the expected value of the developed distribution

Convert the distribution to a payoff under different grading or scoring schemes and compare the resulting expected values

HSS.MD.A.3

HSS.MD.A.3: (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.