Math concepts used: Coin-toss based probability distributions, normal distribution.
Background: #FireGeno is a Twitter meme made popular by several UConn sports-centric tweeters. Geno, of course, is Geno Auriemma, the head coach of UConn women's basketball team since 1985. In light of the team's decades-long dominance (national champions in 1995, 2000, 2002, 2003, 2004, 2009, 2010, 2013, 2014, 2015, 2016), it appears hard to find fault with Geno's coaching ability or his team every year. The #FireGeno tweets thus take pleasure in skewering the occasional foibles of Geno & Co., as the following tweets illustrate.
Lost four games in four seasons even though he had Maya Moore #FireGeno @UConnPuneet
— J-Doug (@RationalPastime) January 14, 2014
Needed 35 minutes to take a 20 point lead #FireGeno @UConnPuneet
— J-Doug (@RationalPastime) March 29, 2014
Some squares are empty. #FireGeno @UConnPuneet @NoEscalators pic.twitter.com/T71VBwDDqV
— J-Doug (@RationalPastime) November 5, 2014
At least two years away from this list #FireGeno @RationalPastime @NoEscalators pic.twitter.com/0sZle7SJA8
— Puneet Nanda (@UConnPuneet) July 5, 2015
What I did: In the spirit of the #FireGeno instigators, I decided to create a set of hypothetical conditions under which Geno may be fired. At this point students were focused on learning all the important probability distributions, so it was natural that one part be devoted to discrete distributions (binomial and negative binomial), and another part to continuous distributions (normal).
Source: The statistics for the margin of victory mentioned at the top of the problem is accurate. See the official NCAA web site for example.
Level of difficulty: Medium. This is a word problem meant to test whether the student understands the various probability distributions and their significance.
Acknowledgements: Many thanks to @UConnPuneet and @RationalPastime for starting the hashtag and for providing the inspiration behind this problem.