Two-dice horse race

Foster, Colin; Martin, David

Abstract

In this article we analyse the “two-dice horse race” task often used in lower secondary school, in which two ordinary dice are thrown repeatedly and each time the sum of the scores determines which horse (numbered 1 to 12) moves forwards one space. The process is repeated until one horse crosses the finishing line a fixed number of spaces away. We examine the difficulties involved in calculating the probability of any particular horse winning the race and carry out a simulation to estimate these probabilities. We conclude that while this task might be a helpful way to introduce sample space diagrams, great care is needed in interpreting the outcome of the race. The greater probability of obtaining a total score of 7 on a single throw of two dice is only partly responsible for horse 7’s greater chance of winining, since the length of the track is also important.

Citation

Foster, C., & Martin, D. (2016). Two-dice horse race. Teaching Statistics, 38(3), 98-101. https://doi.org/10.1111/test.12108

• Journal Article Type: Article
• Acceptance Date: Apr 27, 2016
• Online Publication Date: May 20, 2016
• Publication Date: Aug 3, 2016
• Deposit Date: May 9, 2016
• Publicly Available Date: May 23, 2016
• Journal: Teaching Statistics
• Print ISSN: 0141-982X
• Electronic ISSN: 1467-9639
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 38
• Issue: 3
• Pages: 98-101
• DOI: https://doi.org/10.1111/test.12108
• Public URL: https://nottingham-repository.worktribe.com/output/806712
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1111/test.12108/abstract
• Additional Information: This is the peer reviewed version of the following article: Foster, C., and Martin, D. (2016) Two-dice horse race. TEST, 38: 98–101 doi: 10.1111/test.12108, which has been published in final form at: http://onlinelibrary.wiley.com/doi/10.1111/test.12108/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.