Question

A school offers three types of clubs: sports, arts, and gaming. By the end of the first week of school 100 students signed up. Some students signed up for more than one club. There were 70 signups for sports, 24 signups for arts, and 21 signups for gaming. There were 11 students that signed up for sports and arts, 5 students that signed up for arts and gaming, 9 students that signed up for gaming and sports, and 10 students that signed for all three clubs.

(a)	[3 marks] If a student is chosen at random, what is the probability that the student is in only one club?

(b)	[2 marks] If 5 different students are chosen at random, what is the probability that at least one student is in two or more clubs?

Answer 1

(a) Number of students belonging to exactly one club = (70 + 24 + 21) - (11 + 5 + 9) - 10 = 80.

Hence, the probability of finding a student who belongs to exactly one club = 80/100 = 0.8

(b) Number of students who are part of two or more clubs = (11 + 5 + 9) - 10 = 15.

The probability that a selected student will be part of two or more clubs = 15/100 = 0.15

The probability that at least one out of 5 students are part of two or more clubs = 1 - The probability that none of the 5 students are part of two or more clubs = 1 - = 1 - 0.4437 = 0.5563.