Question

In a school of 330 students, 85 of them are in the drama club, 200 of them are in a sports team and 60 students do drama and sports.
Find the probability that a student chosen at random isn’t in the drama club or in a sports team.

Answer 1

Let's denote students in D = in the drama club , S = in a sports team 
P(D) = 85/330 
P(S) = 200/330 

P(D and S) = 60/300 

P(D or S) = P(D) + P(S) - P(D and S)  = 85/330 + 200/330 - 60/330 = 15/22 

P(neither D nor S) = 1- 15/22 = 7/22