Question

At Lincoln High​ School, 6 students are members of both the Chess Club and the Math Club. There are 20 students in the Math​ Club, 12 students in the Chess​ Club, and 400 students in the entire school. Find the probability that a student chosen at random belongs to the Chess Club or the Math Club

Answer 1

P(C or M) = P(C) + P(M) - P(C and M)

= 12/400 + 20/400 - 6/400

= 26/400 or 0.065

The answer is: P(C or M) = 0.065

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Answer 2

The probability that a student is chosen at random belongs to the Chess Club or the Math Club is 0.065.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

6 students are members of both the Chess Club and the Math Club.

There are 20 students in the Math​ Club, 12 students in the Chess​ Club, and 400 students in the entire school.

The probability that a student is chosen at random belongs to the Chess Club P(C) = 12/400

The probability that a student is chosen at random belongs to the Math Club P(M) = 20/400

The probability that a student is chosen at random belongs to both the Chess Club and the Math Club

P(C ∪ M) = 6/400

The probability that a student chosen at random belongs to the Chess Club or the Math Club

P(C ∩ M) = P(C) + P(M) - P(C ∪ M)

= 12/400 + 20/400 - 6/400

= 26/400

= 0.065

The answer is P(C ∩ M) = 0.065

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