Question

Suppose that your boss must choose four employees in your office to attend a conference in Jamaica, Because all 14 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Samuel Emma, and Paul are chosen?

Answer 1

The probability that you, Samuel, Emma, and Paul are chosen to attend a conference can be found by calculating the reciprocal of the number of ways to choose 4 employees out of 14. This is a combinatorial probability problem.

Step-by-step explanation:

The question asks for the probability that you, Samuel, Emma, and Paul are chosen to attend a conference. This is a classic example of a combinatorial probability question, often dealt with in mathematics, particularly in the area of statistics and probability.

To calculate the probability, note there are 14 employees in total and 4 need to be chosen. The probability that any specific group of 4 employees is chosen out of 14 can be calculated by first determining the number of ways to choose 4 people out of 14 (a combination). This is denoted as "14 choose 4" and calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and ! signifies a factorial.

Once you have the total number of combinations of 4 employees out of 14, you seek the probability that a specific group of four (you, Samuel, Emma, and Paul) is chosen. There is only one way to choose this specific group, since you are not considering the order in which their names are drawn, only that they are drawn.

So the probability is simply 1 divided by the number of ways to draw any group of 4 from 14, which is 1/C(14, 4). Calculate the value of C(14, 4) which is 14!/(4!(14-4)!) = 14!/(4!10!) and then take its reciprocal to find the desired probability.