By Michael D. Larsen (Saint Michael's College)
Probability teaches reasoning about computing the chances of events under assumptions. Basic examples illustrate implications of mutual exclusivity and independence of events. Real world questions often have more complexity that basic examples used in high school and undergraduate courses. They are more challenging, but they can be more interesting and fulfilling to solve. Experience with more complex problems can help solidify ideas and should increase performance on simpler problems. This talk presents an example of couples getting together for a social gathering after vaccination for a disease. The vaccinations do not give 100% immunity. What is the chance of a member of a couple becoming infected by a member of another couple who is infected but non-symptomatic for the disease? The problem illustrates the importance of assumptions and the challenge of moving from small to large versions of a problem.