Calculating the Number of Ways to Choose Three Comedies

Oct 13, 2025 by magicalceylontours.com 52 views

Introduction

Christina is preparing for a vacation and needs to choose three movies from a diverse collection of action, science fiction, and comedy films. The selection process involves choosing three movies out of a total of nine action movies, seven science fiction movies, and four comedies. In this scenario, we need to determine the probability of Christina choosing three comedies. To do this, we must first understand the concept of probability and how it applies to this situation.

What is Probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In the context of Christina's movie selection, we want to find the probability of choosing three comedies out of the available options.

Calculating Probability

To calculate the probability of choosing three comedies, we need to consider the total number of ways Christina can select three movies from the entire collection. This can be calculated using the combination formula:

nCr = n! / (r!(n-r)!)

where n is the total number of items, r is the number of items to be chosen, and ! represents the factorial function.

In this case, the total number of movies is 9 (action) + 7 (science fiction) + 4 (comedy) = 20. Christina needs to choose 3 movies, so we can calculate the total number of ways to do this:

20C3 = 20! / (3!(20-3)!) = 1140

This means there are 1140 ways to choose three movies from the entire collection.

Calculating the Number of Ways to Choose Three Comedies

Now, we need to calculate the number of ways Christina can choose three comedies from the available four comedies. This can also be calculated using the combination formula:

4C3 = 4! / (3!(4-3)!) = 4

There are 4 ways to choose three comedies from the available four comedies.

Calculating the Probability

Now that we have the total number of ways to choose three movies and the number of ways to choose three comedies, we can calculate the probability of choosing three comedies:

Probability = (Number of ways to choose three comedies) / (Total number of ways to choose three movies) = 4 / 1140 = 1/285

Conclusion

In conclusion, the probability that Christina will choose three comedies can be expressed as 1/285. This is the probability of choosing three comedies from the available four comedies, given that Christina is choosing three movies from the entire collection.

Answer

The correct answer is:

A. The probability that Christina will choose three comedies can be expressed as 1/285.

Discussion

Introduction

In our previous article, we explored the concept of probability in the context of Christina's movie selection. We calculated the probability of choosing three comedies from a diverse collection of action, science fiction, and comedy films. In this article, we will provide a Q&A guide to help you better understand the concept of probability and how it applies to real-world scenarios.

Q: What is probability?

A: Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Q: How is probability calculated?

A: Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In the context of Christina's movie selection, we calculated the probability of choosing three comedies by dividing the number of ways to choose three comedies by the total number of ways to choose three movies.

Q: What is the difference between probability and chance?

A: Probability and chance are often used interchangeably, but they have different meanings. Probability refers to the likelihood of an event occurring, while chance refers to the occurrence of an event. For example, the probability of rolling a six on a fair die is 1/6, but the chance of rolling a six is the actual outcome of the roll.

Q: Can probability be expressed as a percentage?

A: Yes, probability can be expressed as a percentage by multiplying the probability by 100. For example, if the probability of choosing three comedies is 1/285, it can be expressed as a percentage as follows:

(1/285) x 100 = 0.35%

Q: What is the concept of independent events?

A: Independent events are events that do not affect each other. For example, flipping a coin and rolling a die are independent events, as the outcome of one event does not affect the outcome of the other event.

Q: How is the probability of independent events calculated?

A: The probability of independent events is calculated by multiplying the probabilities of each event. For example, if the probability of flipping a coin is 1/2 and the probability of rolling a die is 1/6, the probability of both events occurring is:

(1/2) x (1/6) = 1/12

Q: What is the concept of dependent events?

A: Dependent events are events that affect each other. For example, drawing a card from a deck and then drawing another card from the same deck are dependent events, as the outcome of the first event affects the outcome of the second event.

Q: How is the probability of dependent events calculated?

A: The probability of dependent events is calculated by considering the effect of one event on the other. For example, if the probability of drawing a card from a deck is 1/52 and the probability of drawing another card from the same deck is 1/51, the probability of both events occurring is:

(1/52) x (1/51) = 1/2652

Conclusion

In conclusion, probability is a fundamental concept in mathematics that helps us understand the likelihood of events occurring. By understanding the concepts of probability, independent events, and dependent events, we can better navigate real-world scenarios and make informed decisions.

Frequently Asked Questions

Q: What is the probability of choosing three comedies from a collection of 20 movies? A: The probability is 1/285.
Q: How is probability calculated? A: Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Q: What is the difference between probability and chance? A: Probability refers to the likelihood of an event occurring, while chance refers to the occurrence of an event.
Q: Can probability be expressed as a percentage? A: Yes, probability can be expressed as a percentage by multiplying the probability by 100.