Binomial Probabilities

For college basketball fans, there’s nothing better than March Madness! This annual sporting event starts next week and is always full of excitement and surprises. While the tournament was canceled last year because of the pandemic, this year the NCAA is moving forward with limited fan attendance.

The tournament is single-elimination (winner advances, loser goes home), and the matchups are shown as a tree diagram (called a “bracket”). Millions of people try to predict the outcomes every year, and so far, no one has chosen the winner of every game correctly. Why is a perfect bracket so elusive?

The Binomial Probabilities Gizmo can help you answer that question. When a team plays a game, there are two outcomes: a win (success) or a loss (failure). One way you can use the Gizmo is to model the probability that a certain team will win 4 games in the tournament. For example, if a team has an 80% chance of winning each game, they have a 41% chance of winning all 4 games.

The Gizmo can also help you find the probability of choosing the winner of all 63 tournament games. For example, if you have a 50% chance of predicting the winner, use the Gizmo to find the likelihood of getting up to 5 correct predictions in a row. Then extrapolate from there – how likely are 63 successes in a row?