Question 1121415: A basketball team is down by 2 points with only a few seconds remaining in the game. There’s a 50% chance that the team will be able to make a 2-point shot and tie the game, compared to a 30% chance that it will make a 3-point shot and win. If the game ends in a tie, the game continues to overtime. In overtime, the team has a 50% chance of winning. What should the coach do, go for the 2-point shot or the 3-point shot? Be sure to identify any assumptions you make.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Assume that the percentages are for anybody's shooting, and that overtime percentages are not a function of fatigue one way or the other. This is a mathematical construct; the type of play that is set up and executed may not take place, each play has its own probability, and the shooter does, too.
If they make a 2-pointer, with 50% probability, they go into overtime and have a 50% chance of winning. If the two shots are independent, not a bad assumption, the product, 25%, is the probability of winning. There is a 30% probability of making the winning 3-point shot, and that is a better chance.
The other team can win two ways: by not allowing the score in regulation and by winning in overtime, should they lose in regulation. They have a 75% chance of ultimately winning, which drops to 70% if a 3-point shot is attempted.
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