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# Elementary Probability

• ### Song: Probability

A song to teach various concepts in probability. Written by Mary Pat Campbell for Mathcamp 2002 at Colorado College. May be sung to the tune of "Take a Chance on Me" by ABBA. Musical accompaniment realization by Joshua Lintz and vocals by Mariana Sandoval from University of Texas at El Paso.

• ### Quote: Plum on Probability

I failed math twice, never fully grasping probability theory. I mean, first off, who cares if you pick a black ball or a white ball out of the bag? And second, if you're bent over about the color, don't leave it to chance. Look in the damn bag and pick the color you want. is a quote by the fictional bounty hunter Stephanie Plum; a character of American novelist Janet Evanovich (1943-). The quote is from the 2002 novel "Hard Eight."

• ### Cartoon: The Pollsters

A cartoon to teach about the interpretation of confidence statements. The cartoon plays on the idea of what would happen if the same process was repeated over-and-over again. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.

• ### Song: Roll a Pair-a-Dice

The primary themes of this parody involve elementary probability and the importance of graphical summaries. It may be sung to the tune of "Big Yellow Taxi" by Canadian songwriter Joni Mitchell, 1970. Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.

• ### Quote: Boring on Probabilities

There is no alchemy of probabilities that will change ignorance into knowledge. A quote by American psychologist Edwin G. Boring found in "The logic of the Normal Law of error in mental measurement" published in "The American Journal of Psychology" page 1, volume 31, 1920.

• ### Cartoon: The Lottery

A cartoon to teach ideas of elementary probability. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.

• ### Cartoon: Thomas Jefferson's Motivation

A cartoon to teach ideas of conditional probability. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.

• ### Simulating the Effect of Sample Size on the Sampling Distribution of the Mean

This activity allows students to explore the relationship between sample size and the variability of the sampling distribution of the mean. Students use a Java applet to specify the shape of the "parent" distribution and two sample sizes. The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. Students can see both sampling distributions at the same time making them easy to compare. The activity also allows students to determine the probability of extreme sample means for the different sample sizes so that they can discover that small sample sizes are much more likely than large samples to produce extreme values. Keywords: sampling distribution, sample size, simulation
• ### An In-Class Experiment to Estimate Binomial Probabilities

This hands-on activity is appropriate for a lab or discussion section for an introductory statistics class, with 8 to 40 students. Each student performs a binomial experiment and computes a confidence interval for the true binomial probability. Teams of four students combine their results into one confidence interval, then the entire class combines results into one confidence interval. Results are displayed graphically on an overhead transparency, much like confidence intervals would be displayed in a meta-analysis. Results are discussed and generalized to larger issues about estimating binomial proportions/probabilities.
• ### Independent Samples t-Test: Chips AhoyŒ¬ vs. Supermarket Brand

In this hands-on activity, students count the number of chips in cookies in order to carry out an independent samples t-test to see if Chips AhoyŒ¬ cookies have a higher, lower, or different mean number of chips per cookie than a supermarket brand. First there is a class discussion that can include concepts about random samples, independence of samples, recently covered tests, comparing two parameters with null and alternative hypotheses, what it means to be a chip in a cookie, how to break up the cookies to count chips, and of course a class consensus on the hypotheses to be tested. Second the students count the number of chips in a one cookie from each brand, and report their observations to the instructor. Third, the instructor develops the independent sample t-test statistic. Fourth, the students carry out (individually or as a class) the hypothesis test, checking the assumptions on sample-size/population-shape.