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In the 2005 Conference-USA Tournament game, Memphis player Darius Washington Jr. was fouled at the buzzer during a three-point shot. With his team down by two to Louisville, he stepped up to the foul line for three shots.

In this lesson, students will compute the probabilities of a win, loss, or tie for Memphis. They will also determine whether or not it was smart for Louisville to foul at the buzzer, and will investigate the conditions when fouling at the buzzer in a close game makes sense.

Students will

  • Calculate the probability of a win, loss, or tie when a player has three free throws and his team is down by two, and then after the player has taken his first and second shots
  • Calculate the conditional probability of a win or loss for the defensive team, given that they foul or don't foul

Before you begin

Students should know what it means for events to be independent, and should be able to calculate the compound probability of independent events. For example, if a player has a 72% free throw percentage, they should be able to explain why the player’s probability of making three consecutive free throws is 0.723. An understanding of conditional probabilities and Bernoulli trials is also helpful, though not necessary. Finally, students will be asked to generalize their calculations with algebraic expressions.

Common Core Standards

Content Standards
Mathematical Practices


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