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

7/22

Explanation:

330 students total

200 - 60 = 140 is entered into Drama Club

60 in intersect for both

85-60 = 25 for Drama

25+60+140 = 225/330 do both sport and drama

330-225 = 105 = 105/330 do not do any sports or drama

105 is put in the outer box.

105/330 can be simplified by choice =21/66 = 7/22

Answer 2

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