Two Classmates, Aisha And Brandon, Want To Attend Two School Activities Over The Coming Weekend. They Have One Parking Pass Between Them. The Probabilities That The Classmates Will Attend Each Event Are Shown In The

Mar 1, 2025 by ADMIN 216 views

**Two Classmates, One Parking Pass: A Probability Puzzle**

Introduction

In the world of probability, everyday situations can often be turned into mathematical problems. This is exactly what we have in the scenario of Aisha and Brandon, two classmates who want to attend two school activities over the coming weekend. However, they have only one parking pass between them, which creates a constraint that affects their ability to attend both events. In this article, we will explore the probabilities of Aisha and Brandon attending each event and how they can make the most of their limited parking pass.

The Problem

Aisha and Brandon have two school activities to attend over the coming weekend: a concert and a football game. The probabilities that they will attend each event are as follows:

Aisha will attend the concert with a probability of 0.6
Aisha will attend the football game with a probability of 0.4
Brandon will attend the concert with a probability of 0.7
Brandon will attend the football game with a probability of 0.3

They have only one parking pass between them, which means that if one of them attends an event, the other cannot attend the same event. However, they can attend different events. The question is, what is the probability that Aisha and Brandon will attend both events?

Calculating the Probabilities

To solve this problem, we need to calculate the probabilities of Aisha and Brandon attending both events. We can do this by using the concept of conditional probability. Conditional probability is a measure of the probability of an event occurring given that another event has occurred.

Let's define the following events:

A: Aisha attends the concert
B: Aisha attends the football game
C: Brandon attends the concert
D: Brandon attends the football game

We are given the following probabilities:

P(A) = 0.6
P(B) = 0.4
P(C) = 0.7
P(D) = 0.3

We want to find the probability that Aisha and Brandon will attend both events. This can be represented as P(A ∩ C) or P(B ∩ D).

To calculate P(A ∩ C), we need to find the probability of Aisha attending the concert and Brandon attending the concert. We can do this by multiplying the probabilities of Aisha attending the concert and Brandon attending the concert:

P(A ∩ C) = P(A) × P(C) = 0.6 × 0.7 = 0.42

Similarly, we can calculate P(B ∩ D) by multiplying the probabilities of Aisha attending the football game and Brandon attending the football game:

P(B ∩ D) = P(B) × P(D) = 0.4 × 0.3 = 0.12

The Final Answer

So, what is the probability that Aisha and Brandon will attend both events? We have calculated two possible scenarios:

P(A ∩ C) = 0.42: Aisha attends the concert and Brandon attends the concert
P(B ∩ D) = 0.12: Aisha attends the football game and Brandon attends the football game

However, we are not done yet. We need to consider the fact that they have only one parking pass between them. This means that if one of them attends an event, the other cannot attend the same event. Therefore, we need to subtract the probability of Aisha and Brandon attending the same event from the total probability.

The total probability is the sum of the probabilities of Aisha and Brandon attending both events:

P(A ∩ C) + P(B ∩ D) = 0.42 + 0.12 = 0.54

However, we need to subtract the probability of Aisha and Brandon attending the same event. This can be represented as P(A ∩ B) or P(C ∩ D).

To calculate P(A ∩ B), we need to find the probability of Aisha attending the concert and Brandon attending the concert, or Aisha attending the football game and Brandon attending the football game. However, since they have only one parking pass between them, they cannot attend the same event. Therefore, P(A ∩ B) = 0.

Similarly, P(C ∩ D) = 0.

So, the final answer is:

P(A ∩ C) + P(B ∩ D) - P(A ∩ B) - P(C ∩ D) = 0.54 - 0 - 0 = 0.54

Conclusion

In conclusion, the probability that Aisha and Brandon will attend both events is 0.54. This means that there is a 54% chance that they will attend both events. However, we need to consider the fact that they have only one parking pass between them, which means that if one of them attends an event, the other cannot attend the same event.

Real-World Applications

This problem may seem trivial, but it has real-world applications in many fields, such as:

Business: In a business setting, employees may have limited resources, such as a limited number of parking spots or a limited budget. This problem can be used to model the probability of employees attending meetings or events.
Finance: In finance, investors may have limited resources, such as a limited amount of money to invest. This problem can be used to model the probability of investors making investments.
Healthcare: In healthcare, patients may have limited resources, such as a limited number of hospital beds or a limited budget for medical treatment. This problem can be used to model the probability of patients receiving medical treatment.

Final Thoughts

Introduction

In our previous article, we explored the probabilities of Aisha and Brandon attending two school activities over the coming weekend. We calculated the probability that they will attend both events and considered the fact that they have only one parking pass between them. In this article, we will answer some frequently asked questions about the problem and provide additional insights.

Q&A

Q: What is the probability that Aisha will attend the concert?

A: The probability that Aisha will attend the concert is 0.6.

Q: What is the probability that Brandon will attend the football game?

A: The probability that Brandon will attend the football game is 0.3.

Q: Can Aisha and Brandon attend the same event?

A: No, they cannot attend the same event because they have only one parking pass between them.

Q: How did you calculate the probability that Aisha and Brandon will attend both events?

A: We used the concept of conditional probability to calculate the probability that Aisha and Brandon will attend both events. We multiplied the probabilities of Aisha attending the concert and Brandon attending the concert, and the probabilities of Aisha attending the football game and Brandon attending the football game.

Q: What is the total probability that Aisha and Brandon will attend both events?

A: The total probability that Aisha and Brandon will attend both events is 0.54.

Q: Why did you subtract the probability of Aisha and Brandon attending the same event from the total probability?

A: We subtracted the probability of Aisha and Brandon attending the same event from the total probability because they have only one parking pass between them. This means that if one of them attends an event, the other cannot attend the same event.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in many fields, such as business, finance, and healthcare. For example, in a business setting, employees may have limited resources, such as a limited number of parking spots or a limited budget. This problem can be used to model the probability of employees attending meetings or events.

Q: Can you provide more examples of how this problem can be used in real-world scenarios?

A: Here are a few examples:

Business: A company has a limited number of conference rooms and a limited number of employees who can attend meetings. The company wants to know the probability that all employees will attend a meeting.
Finance: An investor has a limited amount of money to invest in the stock market. The investor wants to know the probability that they will make a profit.
Healthcare: A hospital has a limited number of beds and a limited number of patients who can be treated. The hospital wants to know the probability that all patients will receive treatment.

Conclusion

In conclusion, the problem of Aisha and Brandon attending two school activities over the coming weekend is a classic example of a probability puzzle. By using the concept of conditional probability, we can calculate the probability that Aisha and Brandon will attend both events. This problem has real-world applications in many fields, such as business, finance, and healthcare. We hope that this article has provided additional insights and examples of how this problem can be used in real-world scenarios.

Additional Resources

For more information on probability and statistics, please visit the following resources:

Khan Academy: Khan Academy has a comprehensive course on probability and statistics that covers topics such as conditional probability, Bayes' theorem, and hypothesis testing.
MIT OpenCourseWare: MIT OpenCourseWare has a course on probability and statistics that covers topics such as probability distributions, statistical inference, and regression analysis.
Wikipedia: Wikipedia has a comprehensive article on probability and statistics that covers topics such as probability theory, statistical inference, and data analysis.