# Statistics, probability, basketball foul shots

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In summary, the probability that at least 8 out of 10 team members make a successful shot is 1.944, using the binomial distribution and considering the rule for 'AND' probabilities.
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## Homework Statement

Records show that 72% of basketball foul shots attempted are successfully made during practice. Today, each of the 10 members of the team gets a practice shot. What is the probability that at least 8 team members make the shot successfully?

## The Attempt at a Solution

(8/10 * .72) + (9/10 * .72) + (10/10 * .72) = 1.944

Try using the binomial distribution.

Consider the rule for figuring 'AND' probabilities.

For example, what is the probability that two coin flips in a row will both be tails?

0.5 X 0.5 = 0.25 = 25%.

So there is also a 25% chance both will be tails.

Since all the probabilities must add to 100%, the chance of one flip being heads and the other tails is 50%.

## 1. What is the role of statistics in basketball?

Statistics play a crucial role in basketball by providing insights into the performance of individual players and teams. They can help coaches make strategic decisions, track player development, and identify areas for improvement.

## 2. How is probability used in basketball?

Probability is used in basketball to predict the likelihood of a certain outcome, such as a team winning a game or a player making a shot. It can also be used to analyze data and make informed decisions about player rotations and game strategies.

## 3. What is the success rate of basketball foul shots?

The success rate of basketball foul shots varies depending on the level of play. In the NBA, the average free throw percentage is around 75%, while in college basketball it is around 69%. However, individual players may have higher or lower success rates based on their skill and experience.

## 4. How do statistics impact a team's performance in basketball?

Statistics can have a significant impact on a team's performance in basketball. By analyzing data on shooting, rebounding, turnovers, and other key metrics, coaches can identify areas for improvement and make strategic decisions to improve their team's chances of winning.

## 5. Can statistics predict the outcome of a basketball game?

While statistics can provide valuable insights and predictions, they cannot guarantee the outcome of a basketball game. Variables such as team chemistry, injuries, and game-time decisions can all impact the final result. However, statistics can help inform strategic decisions and give an indication of a team's strengths and weaknesses.

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