McGraw-Hill Education GRE 2019

SOLUTION: Since the event has only two outcomes, the probability of a and the

probability of b must add to 1. Thus p 3 + p 5 = 1. To solve for p, multiply across

the equation by 15:

5 p + 3p = 15

8 p = 15

p =^158

Probability of Multiple Events

In the previous example, you looked at the probability of a single event occurring

(selecting a black marble). Tougher probability questions will concern the

probability that multiple events will occur. These questions will take two forms:

probability questions with “and” and probability questions with “or.”

Probability with “or”: Add Them Up

If a probability question concerns the likelihood that one event or another event

will happen, add up the probabilities of each event. For example:

In a certain bookcase, 10 books are about science, 8 are about literature, 5 are

about history, and 2 are about psychology. If a book is selected at random,

what is the probability that the book is about science or history?

A 0.08

B 0.2

C 0.3

D 0.4

E 0.6

SOLUTION: Two different events, a science book or history book, would satisfy

the desired outcome. Thus to determine the number of desired outcomes,

you should add the number of science books and the number of history

books: 10 + 5 = 15. The total number of outcomes is the sum of the books:

10 + 8 + 5 + 2 = 25. The probability of selecting a science book or history

book is thus^1525 =^35 = 0.6. The correct answer is E.

356 PART 4 ■ MATH REVIEW

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