Ohio Resource Center
Content Supports - Activities and rich problems
The Cereal Box Problem
Discipline
Mathematics
9, 10, 11, 12
Professional Commentary

Students explore the Cereal Box Problem first by estimating an answer, then modeling the problem with manipulatives and collecting data for the class, and finally using a computer program to model the problem and determine the theoretical expected value. This mathematically rich problem was prepared by the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools developed by the Ohio Department of Education. (author/sw)

Common Core State Standards for Mathematics
High School - Statistics and Probability
Using Probability to Make Decisions
Calculate expected values and use them to solve problems
HSS-MD.A.1
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions
HSS-MD.A.2
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
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.
HSS-MD.A.4
(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
Ohio Mathematics Academic Content Standards (2001)
Data Analysis and Probability Standard
Benchmarks (8–10)
I.
Design an experiment to test a theoretical probability, and record and explain results.
J.
Compute probabilities of compound events, independent events, and simple dependent events.
K.
Make predictions based on theoretical probabilities and experimental results.
11.
Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities.
8.
Describe, create and analyze a sample space and use it to calculate probability.
10.
Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.