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9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 3.2, Problem 16E

Textbook Problem

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Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area. 25% of all homeowners are insured against earthquake damage. Four homeowners arc to be selected at random: let X denote the number among the four who have earthquake insurance.

**a.**Find the probability distribution of*X*. [*Hint:*Let*S*denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.25)(.75)(.25)(.25) and associated*X*value 3. There are 15 other outcomes.]**b.**Draw the corresponding probability histogram.**c.**What is the most likely value for*X*?**d.**What is the probability that at least two of the four selected have earthquake insurance?

**a.**

To determine

Find the probability distribution of *X*.

**Given info:**

Some parts of California are particularly earthquake-prone. In a metropolitan area, 25% of all homeowners are insured against earthquake damage. Four home owners are selected at random. Let *X* be the number among the four who have earthquake insurance.

**Calculation:**

Let*S* denotes a homeowner who has insurance and *F* denotes a homeowner who has not insurance.

Thus,

The possible values of *X*

The sample space is:

For

For

**b.**

To determine

Draw the corresponding probability histogram.

**c.**

To determine

Find the most likely value for *X*.

**d.**

To determine

Find the probability that at least two of the four selected have earthquake insurance.

Probability and Statistics for Engineering and the Sciences

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