With seconds left in a championship basketball game, Tara and Emek helped evaluate two possible plays that could produce the two points their team needed. From earlier games, they built a probability model for each sequence. In Play A, the opening pass reached the intended player 85% of the time. When that pass succeeded, the player made the shot 60% of the time. Tara calculated the probability of completing both events as 0.85 times 0.60 = 0.51. Play B used a more difficult pass that succeeded 75% of the time, but after a successful pass, the shooter scored 72% of the time. Emek found its overall success probability: 0.75 times 0.72 = 0.54. Although Play A had the more reliable pass, its complete sequence was less likely to produce the needed basket. They checked that the shooting probabilities were conditional on successful passes rather than separate independent events. Since 54% exceeded 51%, Tara and Emek recommended Play B. The team followed the higher-probability plan for its final possession.




