A basketball team is down by 2 points with only a few seconds remaining in the game. There is a 60% 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. In overtime, the team has a 60% 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.

Assuming that the outcomes are independent, the coach should have the team go for the 2 point shot. What is the chance of making the 2 point shot and winning overtime?

Question

02-11-2019
Mathematics

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A basketball team is down by 2 points with only a few seconds remaining in the game. There is a 60% 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. In overtime, the team has a 60% 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.

Assuming that the outcomes are independent, the coach should have the team go for the 2 point shot. What is the chance of making the 2 point shot and winning overtime?

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Answer:

This means that the coach should have the team going for the 2 point shot. There is a 36% probability of making the 2 point shot and winning overtime.

Step-by-step explanation:

We have these following probabilities:

A 60% probability of tying the game on a 2 point shot. In this case, the game goes to overtime, in which the team has a 60% probability of winning.

A 30% probability of making the 3 point shot and winning.

What should the coach do, go for the 2 point shot or the 3 point shot?

In which case the team has a higher probability of winning?

The team has:

A 60% probability of tying the game on a 2 point shot. In this case, the game goes to overtime, in which the team has a 60% probability of winning. So, going for the 2 point shot, the team has a 0.6*0.6 = 0.36 = 36% probability of winning.

Going for the 3 point shot, the team has a 30% probability of winning.

This means that the coach should have the team going for the 2 point shot. There is a 36% probability of making the 2 point shot and winning overtime.