Probability of Selecting Triplets in a Classroom

Oct 13, 2025 by vinooalluri.com 124 views

Probability of Selecting Triplets in a Classroom

In a classroom of 10 students, including triplets Hugh, Stu, and Lou, we are asked to find the probability that Hugh will be the first to give a speech, Stu will be the second, and Lou will be the third. This problem involves the concept of probability, which is a measure of the likelihood of an event occurring. In this case, we need to calculate the probability of a specific sequence of events, where three students are randomly selected from a group of 10.

To solve this problem, we need to understand the concept of permutations and combinations. A permutation is an arrangement of objects in a specific order, while a combination is a selection of objects without regard to order. In this case, we are interested in finding the probability of a specific sequence of events, where Hugh is the first to give a speech, Stu is the second, and Lou is the third.

To calculate the probability of this event, we need to consider the total number of possible outcomes and the number of favorable outcomes. The total number of possible outcomes is the number of ways to select 3 students from a group of 10, which is given by the combination formula:

10C3 = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

This means that there are 120 possible ways to select 3 students from a group of 10.

Now, let's consider the number of favorable outcomes, where Hugh is the first to give a speech, Stu is the second, and Lou is the third. Since the order of selection matters, we need to consider the permutation of the 3 students. The number of permutations of 3 students is given by:

3! = 3 * 2 * 1 = 6

This means that there are 6 possible ways to arrange the 3 students in the order Hugh, Stu, and Lou.

Now, we can calculate the probability of the event by dividing the number of favorable outcomes by the total number of possible outcomes:

P(Hugh, Stu, Lou) = Number of favorable outcomes / Total number of possible outcomes = 6 / 120 = 1/20 = 0.05

Therefore, the probability that Hugh will be the first to give a speech, Stu will be the second, and Lou will be the third is 1/20 or 0.05.

In conclusion, the probability of selecting Hugh, Stu, and Lou in a specific order is 1/20 or 0.05. This problem involves the concept of permutations and combinations, and requires us to calculate the probability of a specific sequence of events. By understanding the concept of permutations and combinations, we can solve this problem and find the probability of the event.

This problem has real-world applications in various fields, such as:

Statistics: Probability is a fundamental concept in statistics, and is used to analyze and interpret data.
Finance: Probability is used to calculate the risk of investments and to determine the likelihood of certain events occurring.
Engineering: Probability is used to design and optimize systems, and to predict the behavior of complex systems.

In our previous article, we discussed the probability of selecting Hugh, Stu, and Lou in a specific order from a group of 10 students. We calculated the probability to be 1/20 or 0.05. In this article, we will answer some frequently asked questions related to this problem.

A: To calculate the probability of selecting any two of the triplets first, we need to consider the number of ways to select 2 students from a group of 3. This is given by the combination formula:

3C2 = 3! / (2! * (3-2)!) = 3! / (2! * 1!) = (3 * 2) / (2 * 1) = 3

This means that there are 3 possible ways to select 2 students from a group of 3. The probability of selecting any two of the triplets first is therefore:

P(any two of the triplets first) = Number of favorable outcomes / Total number of possible outcomes = 3 / 120 = 1/40 = 0.025

A: To calculate the probability of selecting all three of the triplets first, we need to consider the number of ways to select 3 students from a group of 3. This is given by the combination formula:

3C3 = 3! / (3! * (3-3)!) = 1

This means that there is only 1 possible way to select all three of the triplets first. The probability of selecting all three of the triplets first is therefore:

P(all three of the triplets first) = Number of favorable outcomes / Total number of possible outcomes = 1 / 120 = 1/120 = 0.0083

A: To calculate the probability of selecting Hugh, Stu, and Lou in any order, we need to consider the number of ways to arrange the 3 students. This is given by the permutation formula:

3! = 3 * 2 * 1 = 6

This means that there are 6 possible ways to arrange the 3 students. The probability of selecting Hugh, Stu, and Lou in any order is therefore:

P(Hugh, Stu, Lou in any order) = Number of favorable outcomes / Total number of possible outcomes = 6 / 120 = 1/20 = 0.05

A: To calculate the probability of selecting Hugh, Stu, and Lou in a specific order, but with the order of the last two students reversed, we need to consider the number of ways to arrange the 3 students with the order of the last two students reversed. This is given by the permutation formula:

3! = 3 * 2 * 1 = 6

However, since the order of the last two students is reversed, we need to divide the number of permutations by 2 to account for the reversal. Therefore, the number of favorable outcomes is:

6 / 2 = 3

The probability of selecting Hugh, Stu, and Lou in a specific order, but with the order of the last two students reversed, is therefore:

P(Hugh, Stu, Lou in a specific order, but with the order of the last two students reversed) = Number of favorable outcomes / Total number of possible outcomes = 3 / 120 = 1/40 = 0.025

In conclusion, we have answered some frequently asked questions related to the probability of selecting Hugh, Stu, and Lou in a specific order from a group of 10 students. We have calculated the probability of selecting any two of the triplets first, the probability of selecting all three of the triplets first, the probability of selecting Hugh, Stu, and Lou in any order, and the probability of selecting Hugh, Stu, and Lou in a specific order, but with the order of the last two students reversed.