Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE PS – The probability that event M will not occur is 0.8 and the probability that event R will not occur…

The probability that event M will not occur is 0.8 and the probability that event R will not occur…

Solution:

We are given that the probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6, and that events M and R cannot both occur.

We need to determine the probability that either event M or event R will occur.

The probability that event M will occur is 1 – 0.8 = 0.2 = 1/5

The probability that event R will occur is 1 – 0.6 = 0.4 = 2/5

Recall that the formula for the probability of event A or event B occurring is P(A or B) = P(A) + P(B) – P(A and B); therefore:

P(M or R) = P(M) + P(R) – P(M and R).

Since we are told that events M and R cannot both occur, that means P(M and R) = 0 and thus the probability that either event M or event R will occur is:

P(M or R) = 1/5 + 2/5 – 0 = 3/5.

Answer: C

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