Solution Found!
Answer: Some parts of California are particularly
Chapter 3, Problem 16E(choose chapter or problem)
Problem 16E
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 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 probability
(.25)(.75)(.25)(.25) and associated X value 3. There are15 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?
Questions & Answers
QUESTION:
Problem 16E
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 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 probability
(.25)(.75)(.25)(.25) and associated X value 3. There are15 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?
ANSWER:Solution :
Step 1 :
Here they randomly selected one metropolitan area in california, where 25% of all homeowners are insured against earthquake. From that four homeowners are to be selected at random, and X denote the number among four who have earthquake insurance.