Loading...
Digital SAT
Digital SAT Mathematics - Calculator Section

Probability of Membership in Two Clubs

Very Hard Problem Solving And Data Analysis Probability And Statistics

In a certain school, the students are enrolled in two clubs: the Science Club and the Math Club. The total number of students in both clubs is 240. Each student is a member of at least one of the two clubs.

Let:

  • $x$ = number of students in the Science Club
  • $y$ = number of students in the Math Club
  • $z$ = number of students in both clubs

The following information is known:

  • There are 80 students in the Science Club who are not in the Math Club.
  • There are 60 students in the Math Club who are not in the Science Club.

Given this information, what is the probability that a randomly selected student from the entire school is a member of both clubs?

Hint

Submitted10.5K
Correct8.2K
% Correct78%