Some parts of California are particularly earthquakeprone.Suppose that in one metropolitan area, 25% of allhomeowners are insured against earthquake damage.Four homeowners are to be selected at random; let Xdenote the number among the four who have earthquakeinsurance.a. Find the probability distribution of X. [Hint: Let Sdenote a homeowner who has insurance and F onewho does not. Then one possible outcome is SFSS,with proba bility (.25)(.75)(.25)(.25) and associated Xvalue 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 fourselected have earthquake insurance?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Some parts of California are particularly earthquakeprone.
Suppose that in one metropolitan area, 25% of all
homeowners are insured against earthquake damage.
Four homeowners are 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 proba bility (.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?

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