A Placekicker For A Football Team Makes Field Goals $55 \%$ Of The Time When Kicking From The 35-yard Line. Assume That Field Goal Attempts Can Be Considered Random Events. Using The Table, What Is The Probability That The Placekicker Will

Introduction

In the game of football, a placekicker's ability to make field goals is a crucial aspect of the team's success. The probability of a placekicker making a field goal from a specific distance can be an important factor in determining the team's strategy and overall performance. In this article, we will explore the probability of a placekicker making field goals from the 35-yard line.

The Problem

A placekicker for a football team makes field goals $55 \%$ of the time when kicking from the 35-yard line. We are asked to find the probability that the placekicker will make a field goal from this distance.

The Solution

To solve this problem, we can use the concept of probability. Since field goal attempts can be considered random events, we can assume that the probability of making a field goal is constant and independent of the number of attempts.

Let's define the probability of making a field goal as $P(FG)$. We are given that $P(FG) = 0.55$. We want to find the probability that the placekicker will make a field goal from the 35-yard line.

Since the probability of making a field goal is constant, we can assume that the probability of making a field goal from the 35-yard line is also $0.55$.

The Probability of Making a Field Goal

The probability of making a field goal from the 35-yard line is given by:

$$P(FG_{35}) = P(FG) = 0.55$$

This means that the placekicker has a $55 \%$ chance of making a field goal from the 35-yard line.

The Probability of Missing a Field Goal

Since the probability of making a field goal is $0.55$, the probability of missing a field goal is:

$$P(MG) = 1 - P(FG) = 1 - 0.55 = 0.45$$

This means that the placekicker has a $45 \%$ chance of missing a field goal from the 35-yard line.

The Probability of Making a Field Goal in a Specific Number of Attempts

We can also find the probability of making a field goal in a specific number of attempts. For example, let's say we want to find the probability of making a field goal in 3 attempts.

We can use the binomial distribution to find the probability of making a field goal in 3 attempts:

$$P(FG_{3}) = \binom{3}{1} (0.55)^1 (0.45)^2 = 0.3025$$

This means that the placekicker has a $30.25 \%$ chance of making a field goal in 3 attempts from the 35-yard line.

The Probability of Making a Field Goal in a Specific Number of Attempts with a Specific Number of Misses

We can also find the probability of making a field goal in a specific number of attempts with a specific number of misses. For example, let's say we want to find the probability of making a field goal in 3 attempts with 1 miss.

We can use the binomial distribution to find the probability of making a field goal in 3 attempts with 1 miss:

$$P(FG_{3}, MG_{1}) = \binom{3}{1} (0.55)^1 (0.45)^2 = 0.3025$$

This means that the placekicker has a $30.25 \%$ chance of making a field goal in 3 attempts with 1 miss from the 35-yard line.

Conclusion

In this article, we explored the probability of a placekicker making field goals from the 35-yard line. We found that the placekicker has a $55 \%$ chance of making a field goal from this distance. We also found the probability of making a field goal in a specific number of attempts and the probability of making a field goal in a specific number of attempts with a specific number of misses.

References

• [1] Wikipedia. (2023). Placekicker. Retrieved from https://en.wikipedia.org/wiki/Placekicker
• [2] ESPN. (2023). NFL Field Goal Percentage. Retrieved from https://www.espn.com/nfl/statistics/_/stat/field-goal-percentage

Table of Contents

1. Introduction
2. The Problem
3. The Solution
4. The Probability of Making a Field Goal
5. The Probability of Missing a Field Goal
6. The Probability of Making a Field Goal in a Specific Number of Attempts
7. The Probability of Making a Field Goal in a Specific Number of Attempts with a Specific Number of Misses
8. Conclusion
9. References
   A Placekicker's Field Goal Probability: Q&A =============================================

Introduction

In our previous article, we explored the probability of a placekicker making field goals from the 35-yard line. We found that the placekicker has a $55 \%$ chance of making a field goal from this distance. In this article, we will answer some frequently asked questions about the probability of a placekicker making field goals.

Q: What is the probability of a placekicker making a field goal from the 40-yard line?

A: Unfortunately, we do not have enough information to determine the probability of a placekicker making a field goal from the 40-yard line. However, we can use the concept of probability to estimate the probability of making a field goal from this distance.

Assuming that the probability of making a field goal is constant and independent of the distance, we can use the following formula to estimate the probability of making a field goal from the 40-yard line:

$$P(FG_{40}) = P(FG) \times \frac{40}{35}$$

Using this formula, we can estimate the probability of making a field goal from the 40-yard line as follows:

$$P(FG_{40}) = 0.55 \times \frac{40}{35} = 0.6286$$

This means that the placekicker has a $62.86 \%$ chance of making a field goal from the 40-yard line.

Q: What is the probability of a placekicker making a field goal from the 50-yard line?

A: Using the same formula as above, we can estimate the probability of making a field goal from the 50-yard line as follows:

$$P(FG_{50}) = 0.55 \times \frac{50}{35} = 0.7857$$

This means that the placekicker has a $78.57 \%$ chance of making a field goal from the 50-yard line.

Q: What is the probability of a placekicker making a field goal in 4 attempts?

A: We can use the binomial distribution to find the probability of making a field goal in 4 attempts:

$$P(FG_{4}) = \binom{4}{1} (0.55)^1 (0.45)^3 = 0.3846$$

This means that the placekicker has a $38.46 \%$ chance of making a field goal in 4 attempts from the 35-yard line.

Q: What is the probability of a placekicker making a field goal in 5 attempts?

A: We can use the binomial distribution to find the probability of making a field goal in 5 attempts:

$$P(FG_{5}) = \binom{5}{1} (0.55)^1 (0.45)^4 = 0.2679$$

This means that the placekicker has a $26.79 \%$ chance of making a field goal in 5 attempts from the 35-yard line.

Q: What is the probability of a placekicker making a field goal in 6 attempts?

A: We can use the binomial distribution to find the probability of making a field goal in 6 attempts:

$$P(FG_{6}) = \binom{6}{1} (0.55)^1 (0.45)^5 = 0.1944$$

This means that the placekicker has a $19.44 \%$ chance of making a field goal in 6 attempts from the 35-yard line.

Q: What is the probability of a placekicker making a field goal in 7 attempts?

A: We can use the binomial distribution to find the probability of making a field goal in 7 attempts:

$$P(FG_{7}) = \binom{7}{1} (0.55)^1 (0.45)^6 = 0.1414$$

This means that the placekicker has a $14.14 \%$ chance of making a field goal in 7 attempts from the 35-yard line.

Conclusion

In this article, we answered some frequently asked questions about the probability of a placekicker making field goals. We estimated the probability of making a field goal from the 40-yard line and the 50-yard line, and we found the probability of making a field goal in 4, 5, 6, and 7 attempts.

References

• [1] Wikipedia. (2023). Placekicker. Retrieved from https://en.wikipedia.org/wiki/Placekicker
• [2] ESPN. (2023). NFL Field Goal Percentage. Retrieved from https://www.espn.com/nfl/statistics/_/stat/field-goal-percentage

Table of Contents

1. Introduction
2. Q: What is the probability of a placekicker making a field goal from the 40-yard line?
3. Q: What is the probability of a placekicker making a field goal from the 50-yard line?
4. Q: What is the probability of a placekicker making a field goal in 4 attempts?
5. Q: What is the probability of a placekicker making a field goal in 5 attempts?
6. Q: What is the probability of a placekicker making a field goal in 6 attempts?
7. Q: What is the probability of a placekicker making a field goal in 7 attempts?
8. Conclusion
9. References