The Total Number of Friends

Oct 13, 2025 by recoveryshake.com 114 views

Probability is a measure of the likelihood of an event occurring. In this case, we are interested in finding the probability that the first two friends to show up at the movie are among Xander's 4 friends he has known since kindergarten.

The Total Number of Friends

Xander has 10 closest friends. This is the total number of possible outcomes when selecting 2 friends from the group.

The Number of Friends Known Since Kindergarten

Xander has known 4 of his 10 closest friends since kindergarten. This is the number of favorable outcomes, as we are interested in finding the probability that the first two friends to show up are among these 4 friends.

Calculating the Probability

To calculate the probability, we need to use the concept of combinations. The number of ways to choose 2 friends from a group of 10 is given by the combination formula:

C(10, 2) = 10! / (2! * (10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45

This means there are 45 possible ways to choose 2 friends from a group of 10.

The number of ways to choose 2 friends from the 4 friends known since kindergarten is given by:

C(4, 2) = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6

This means there are 6 possible ways to choose 2 friends from the 4 friends known since kindergarten.

The Probability

The probability that the first two friends to show up are among Xander's 4 friends he has known since kindergarten is given by:

P = (Number of favorable outcomes) / (Total number of possible outcomes) = C(4, 2) / C(10, 2) = 6 / 45 = 2/15

Therefore, the probability that the first two friends to show up are among Xander's 4 friends he has known since kindergarten is 2/15 or approximately 0.1333.

Conclusion

In this article, we have discussed the concept of probability and how to calculate it using combinations. We have also applied this concept to a real-world scenario, where we wanted to find the probability that the first two friends to show up at a movie are among Xander's 4 friends he has known since kindergarten. The probability is 2/15 or approximately 0.1333.

Frequently Asked Questions

What is the probability that the first two friends to show up are among Xander's 4 friends he has known since kindergarten?
The probability is 2/15 or approximately 0.1333.
How do you calculate the probability using combinations?
The number of ways to choose 2 friends from a group of 10 is given by the combination formula C(10, 2) = 10! / (2! * (10-2)!).
The number of ways to choose 2 friends from the 4 friends known since kindergarten is given by C(4, 2) = 4! / (2! * (4-2)!).
The probability is given by P = (Number of favorable outcomes) / (Total number of possible outcomes).

References

[1] "Probability" by Khan Academy
[2] "Combinations" by Math Is Fun
[3] "Probability and Statistics" by Coursera
Frequently Asked Questions: Understanding Probability =====================================================

In our previous article, we discussed the concept of probability and how to calculate it using combinations. We also applied this concept to a real-world scenario, where we wanted to find the probability that the first two friends to show up at a movie are among Xander's 4 friends he has known since kindergarten. In this article, we will answer some frequently asked questions related to probability.

Q: What is the definition of probability?

A: Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1 that represents the chance of an event happening.

Q: How do you calculate probability?

A: Probability is calculated using the formula:

P = (Number of favorable outcomes) / (Total number of possible outcomes)

Q: What is the difference between probability and odds?

A: Probability and odds are related but distinct concepts. Probability is a measure of the likelihood of an event occurring, while odds represent the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

Q: Can you give an example of how to calculate probability?

A: Let's say we want to find the probability of rolling a 6 on a fair six-sided die. There are 6 possible outcomes (1, 2, 3, 4, 5, and 6), and only 1 of them is a 6. Therefore, the probability of rolling a 6 is:

P = (Number of favorable outcomes) / (Total number of possible outcomes) = 1 / 6 = 0.1667

Q: What is the concept of independent events in probability?

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 does not affect the outcome of the other.

Q: Can you give an example of how to calculate the probability of independent events?

A: Let's say we want to find the probability of flipping a coin and getting heads, and then rolling a die and getting a 6. The probability of flipping a coin and getting heads is 1/2, and the probability of rolling a die and getting a 6 is 1/6. Since these events are independent, we can multiply the probabilities together to get the probability of both events occurring:

P = (Probability of getting heads) * (Probability of getting a 6) = (1/2) * (1/6) = 1/12

Q: What is the concept of conditional probability?

A: Conditional probability is the probability of an event occurring given that another event has occurred. For example, the probability of getting a 6 on a die given that the first roll was a 6 is different from the probability of getting a 6 on a die without any prior information.

Q: Can you give an example of how to calculate conditional probability?

A: Let's say we want to find the probability of getting a 6 on a die given that the first roll was a 6. The probability of getting a 6 on a die is 1/6, and the probability of getting a 6 on a die given that the first roll was a 6 is 1/5 (since there are now 5 remaining outcomes that are not a 6).

Q: What is the concept of Bayes' theorem?

A: Bayes' theorem is a mathematical formula that allows us to update the probability of an event given new information. It is used in many fields, including statistics, machine learning, and artificial intelligence.

Q: Can you give an example of how to use Bayes' theorem?

A: Let's say we want to find the probability that a person has a certain disease given that they have a positive test result. We can use Bayes' theorem to update the probability of the disease given the new information.

Conclusion

In this article, we have answered some frequently asked questions related to probability. We have discussed the concept of probability, how to calculate it, and how to apply it to real-world scenarios. We have also covered the concepts of independent events, conditional probability, and Bayes' theorem. We hope that this article has been helpful in understanding probability and its applications.

References

[1] "Probability" by Khan Academy
[2] "Combinations" by Math Is Fun
[3] "Probability and Statistics" by Coursera
[4] "Bayes' Theorem" by Wikipedia