Question

Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are on the football team and two are on the basketball team. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor randomly selects two of the four wait list students and gives them seats in the class. What is the probability that both students selected play the same sport?

Answer 1

The probability that both wait-listed students selected for the class play the same sport is 1/3 or approximately 33.33%.

Step-by-step explanation:

The subject of the question is mathematics, specifically the area of probability. The question asks for the probability that both students selected from the wait list play the same sport, given that there are two students each from the football team and the basketball team. To solve this, we would consider the combinations in which two students can be selected from the wait list.

We can choose two students from the football team or two students from the basketball team. There are combin(2,2) ways to choose two students from the football team (which is 1 way since we must choose both), and similarly, combin(2,2) ways to select two students from the basketball team (1 way as well). The total number of ways to select any two students out of the four is combin(4,2) (which is the combination of 4 students taken 2 at a time, and the result is 6 ways).

The probability is, therefore, the number of favorable outcomes over the total number of possible outcomes.
Probability = (Number of ways to choose 2 from football team + Number of ways to choose 2 from basketball team) / Total number of ways to choose any 2 students
Probability = (1 + 1) / 6
Probability = 2 / 6
Probability = 1 / 3

So, the probability that both students selected play the same sport is 1/3 or approximately 33.33%.