Probability

  • Summary: Through generating, collecting, displaying, and analyzing data, students are given the opportunity to explore a variety of descriptive statistical techniques and develop an understanding of the distinction between theoretical, subjective, and empirical (or experimental) probabilities. These concepts are developed with activities using Hershey KissesTM and may be extended to introduce the sampling distribution of a sample proportion. The activities are described in M. Richardson and S. Haller. (2002), “What is the Probability of a Kiss? (It's Not What You Think),” Journal of Statistics Education, 10(3), https://www.tandfonline.com/doi/full/10.1080/10691898.2002.11910683

    Specifics: The main activity uses Hershey’s Kisses to explore the concept of probability. Three specific sub-activities are performed such as: 

    1. Students explore the empirical probability that a plain Hershey’s Kiss will land on its flat base when spilled from a cup. 
    2. Students make predictions about the probability of an almond Hershey’s Kisses landing on its base when spilled from a cup, after having experimented with the plain Kisses.
    3. Students explore the properties of the distribution of a sample proportion to see whether the percentages of base landings have a specified distribution and whether they think that the number of Kisses tossed affects the shape or the mean and standard deviation of this distribution.

    (Resource photo illustration by Barbara Cohen, 2020; this summary compiled by Bibek Aryal)

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  • A joke about the meaning of an inequality symbol like ≤ written in February 2020 by Larry Lesser from The University of Texas at El Paso and Dennis Pearl from Penn State University.

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  • A poem written in 2019 by Larry Lesser from The University of Texas at El Paso to discuss the topic of randomness and the lexical ambiguity of the word "random" in statistical versus everyday usage.  The poem is part of a collection of 8 poems published with commentary in the January 2020 issue of Journal of Humanistic Mathematics.

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  • A joke to start a discussion about how probability is used to study uncertainty in real life situations. The joke might depend somewhat on the composition of the audience since understanding the joke relies on knowing that probabilidad is the Spanish word for probability. Also, in delivering the joke it might help to put some emphasis on the last syllable to make this a true "dad joke". The joke was written in 2019 by Larry Lesser from The University of Texas at El Paso.

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  • A cartoon to illustrate the value of statistics in the software that controls many devices.  The cartoon was drawn in 2013 by British cartoonist John Landers based on an idea by Dennis Pearl from Ohio State University.  This item is part of the cartoons and readings from the “World Without Statistics” series that provided cartoons and readings on important applications of statistics created for celebration of 2013 International Year of Statistics.  The series may be found at https://online.stat.psu.edu/stat100/lesson/1/1.4

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  • A cartoon to instigate discussions on the use of random numbers in both designing and analyzing data.The cartoon was used in the October 2018 CAUSE cartoon caption contest and the winning caption was written by Anthony Bonifonte from Denison University. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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  • A cartoon to be used in class discussions that introduce basic queueing theory. The cartoon was used in the August, 2017 CAUSE cartoon caption contest and the winning caption was submitted by Larry Lesser from The University of Texas at El Paso. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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  • A cartoon to aid in discussing Simpson's paradox by providing an illustration that an association seen in smaller groups can reverse direction when the data are aggregated. The cartoon was drawn by Britsh cartoonist John Landers based on idea from Dennis Pearl of Penn State University.

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  • A cartoon to be used as a vehicle to discuss Cornfield’s simple conditions required of a potential confounder to create a Simpson's Paradox situation The cartoon was used in the June 2018 CAUSE Cartoon Caption Contest. This winning caption was submitted by Larry Lesser from The University of Texas at El Paso. The drawing was created by British cartoonist John Landers based on an idea from Dennis Pearl of Penn State University.

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  • A cartoon suitable for use in teaching about Bayes Theorem (an obvious follow-up exercise is to ask what “P(C)” would have to be to make the “Modified Bayes Theorem” correct). The cartoon is number 2059 (October, 2018) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a creative commons attribution-non-commercial 2.5 license.

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