Before the start of the NCAA Men’s Basketball Tournament, which ends next weekend, Warren Buffett offered a prize of one billion dollars to anyone who could create a perfect bracket. It only took 25 games before the last possible winning entry was eliminated, and Buffett’s money was safe.
How many brackets are possible in the tournament, and what are the chances of creating a perfect bracket? Students can explore these questions with the Binomial Probabilities Gizmo.
In this Gizmo, students use tree diagrams to illustrate the possible outcomes of a series of binomial experiments. Students then derive the formula for finding the probability of r successful outcomes in n experiments.
By the way, there are over 9.2 quintillion (9,200,000,000,000,000) possible brackets in the NCAA tournament. Warren Buffett’s money might be safe for a while!