Final answer:
The events of going to college, working full-time, and taking a gap year are not mutually exclusive, as their total exceeds the number of students. The probability of a senior going to college and playing on a sports team is 1/6 or approximately 0.167.
Step-by-step explanation:
In the high school graduating class scenario provided, we are examining mutually exclusive events and the probability of students being involved in certain categories. Mutually exclusive events cannot happen at the same time – that is, if one event occurs, the other cannot. However, the given information indicates that the sum of the students going to college (200), planning to work full-time (40), and taking a gap year (80) exceed the total number of students, which is 300. This suggests that the categories overlap and that some students are counted in more than one category. Thus, these are not mutually exclusive events.
To determine the probability that a senior is going to college and plays sports, we use the information provided. Out of the 200 students going to college, 50 play sports on their school's teams. Since no other conditions are provided, the probability in this context would be simply the number of students going to college and playing sports divided by the total number of students: P(A and B) = 50/300 = 1/6 or approximately 0.167.