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# A study by the National Park Service revealed that 50

ISBN: 9780077384470 64

## Solution for problem 22E Chapter 5

Basic Statistics for Business and Economics | 7th Edition

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Problem 22E

A study by the National Park Service revealed that 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.

a. What is the probability a vacationer will visit at least one of these attractions?

b. What is the probability .35 called?

c. Are the events mutually exclusive? Explain.

Step-by-Step Solution:

Step 1 of 3:

In a study it is found that, 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.

We have to find the probability that a vacationer will visit at least one of theses places.We have to name the probability 0.35.We have to check whether the events are mutually exclusive.

Step 2 of 3:

Let us define the events,

A= { Event that vacationers going to the Rocky Mountain region}

B= { Event that vacationers going to Tetons}

From the given informations:

P(A) = 0.50

P(B) = 0.40

P(AB) = 0.35

(a)

The probability that a vacationer will visit at least one of theses places.

P(AB) = P(A)+ P(B)- P(AB)

= 0.50+0.40-0.35

= 0.55

Therefore, the probability that a vacationer will visit at least one of theses places is 0.55.

Step 3 of 3

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