Probability of making a shot

Oct 13, 2025 by wbrum.org 89 views

The Art of Probability: Unraveling the Mystery of Free-Throw Shots

In the world of basketball, free-throw shots are a crucial aspect of the game. A player's ability to make these shots can make all the difference in the outcome of a game. But have you ever wondered what the probability of a player making or missing a free-throw shot is? In this article, we will delve into the world of probability and explore the concept of free-throw shots.

Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In the case of free-throw shots, the probability of making a shot is usually expressed as a percentage.

We are given that a basketball player makes $85\%$ of his free-throw shots. This means that the probability of him making a free-throw shot is $0.85$ . We are also asked to find the probability that he does NOT make his next free-throw shot.

To find the probability of not making a free-throw shot, we can use the complement rule. The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.

Let $P(M)$ be the probability of making a free-throw shot, and $P(N)$ be the probability of not making a free-throw shot. We are given that $P(M) = 0.85$ . Using the complement rule, we can write:

P(N) = 1 - P(M)

Substituting the value of $P(M)$ , we get:

P(N) = 1 - 0.85

P(N) = 0.15

Therefore, the probability that the basketball player does NOT make his next free-throw shot is $15\%$ .

The result we obtained is quite intuitive. If a player makes $85\%$ of his free-throw shots, it means that he misses $15\%$ of his shots. This is because the total probability of all possible outcomes must add up to 1.

In this article, we used the concept of probability to find the probability of a basketball player not making a free-throw shot. We used the complement rule to find the probability of not making a shot, given the probability of making a shot. The result we obtained is quite intuitive and makes sense in the context of the game of basketball.

The concept of probability is not limited to basketball. It has numerous real-world applications in fields such as finance, engineering, and medicine. For example, in finance, probability is used to calculate the risk of investments, while in engineering, it is used to design and optimize systems.

In conclusion, the concept of probability is a powerful tool that can be used to analyze and understand complex phenomena. In the context of basketball, probability can be used to predict the outcome of games and make informed decisions. We hope that this article has provided a clear and concise introduction to the concept of probability and its applications in basketball.

Probability: A measure of the likelihood of an event occurring.
Complement rule: A rule that states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.
Free-throw shot: A shot taken from the free-throw line in basketball.
Probability of making a shot: The probability of a player making a free-throw shot.
Probability of not making a shot: The probability of a player not making a free-throw shot.

[1] "Probability" by Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Probability
[2] "Complement rule" by Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Complement_rule
[3] "Free-throw shot" by Basketball-Reference.com. Retrieved from https://www.basketball-reference.com/leagues/NBA_2020.html

The author is a mathematics enthusiast with a passion for writing and teaching. They have a strong background in mathematics and statistics, and have written several articles on various topics related to mathematics and probability.
Frequently Asked Questions: Understanding Probability in Basketball

In our previous article, we explored the concept of probability in basketball, specifically in the context of free-throw shots. We used the complement rule to find the probability of a player not making a free-throw shot, given the probability of making a shot. In this article, we will answer some frequently asked questions related to probability in basketball.

A: The probability of a player making a free-throw shot is 85%, which means that they have an 85% chance of making the shot.

A: Using the complement rule, we can find the probability of not making a shot by subtracting the probability of making a shot from 1. So, the probability of not making a shot is 1 - 0.85 = 0.15, or 15%.

A: The probability of making a free-throw shot can change depending on the situation. If the player is under pressure, their probability of making the shot may decrease. However, this is a complex issue that depends on many factors, including the player's experience, skill level, and mental state.

A: Yes, the probability of making a free-throw shot can be affected by external factors, such as the crowd or the referee. For example, if the crowd is cheering and the referee is calling a favorable foul, the player may feel more confident and have a higher probability of making the shot.

A: A player can increase their probability of making a free-throw shot by practicing regularly, developing a consistent shooting form, and staying focused and confident during games.

A: Yes, the probability of making a free-throw shot can be affected by the player's physical and mental state. For example, if the player is tired or injured, their probability of making the shot may decrease. Similarly, if the player is experiencing anxiety or stress, their probability of making the shot may also decrease.

A: A coach or team can use probability to make informed decisions during games by analyzing the probability of different outcomes, such as the probability of making a free-throw shot or the probability of winning a game. This can help them make strategic decisions, such as when to take a shot or when to play defense.

In this article, we answered some frequently asked questions related to probability in basketball. We hope that this article has provided a clear and concise introduction to the concept of probability and its applications in basketball.

Probability: A measure of the likelihood of an event occurring.
Complement rule: A rule that states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.
Free-throw shot: A shot taken from the free-throw line in basketball.
Probability of making a shot: The probability of a player making a free-throw shot.
Probability of not making a shot: The probability of a player not making a free-throw shot.

[1] "Probability" by Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Probability
[2] "Complement rule" by Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Complement_rule
[3] "Free-throw shot" by Basketball-Reference.com. Retrieved from https://www.basketball-reference.com/leagues/NBA_2020.html