Final answer:
The probability that a student chosen at random isn't in the drama club or on a sports team is 7/22. This is found by subtracting the number of students in both activities from the total and then dividing by the number of students in the school.
Step-by-step explanation:
To find the probability that a student chosen at random isn't in the drama club or in a sports team, we can use the principle of inclusion and exclusion. We start by identifying the total number of students, which is 330. The number of students in the drama club is 85, and the number of students in a sports team is 200. Also, there are 60 students who are involved in both drama and sports.
First, we should subtract the number of students involved in drama and sports from each individual group to avoid double-counting:
- Exclusive drama club members: 85 - 60 = 25
- Exclusive sports team members: 200 - 60 = 140
Now, we add the numbers of exclusive members of each group and the ones who are in both:
Total students in drama or sports: 25 (drama) + 140 (sports) + 60 (both) = 225
Next, we'll subtract this number from the total student population to find out how many students aren't in either group:
Students not in drama or sports: 330 - 225 = 105
Finally, we calculate the probability by dividing the number of students not in drama or sports by the total number of students:
Probability(not in drama and not in sports) = 105 / 330
This can be reduced to:
Probability = 7 / 22
Hence, the probability that a student chosen at random is neither in the drama club nor on a sports team is 7/22.