Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 35% 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 that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.35)(0.65)(0.35)(0.35) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.) 1 2 3 4 P(x) (b) Draw the corresponding probability histogram. Probability 0.4 Probability 0.4 0.3 0.3 0.2 0.2 0.1 Number with 0.1 Number with 0.0 earthquake 0.0 earthquake 0 1 2 3 4 0 1 2 3 4 insurance insurance Probability Probability 0.4 0.4 0.3 0.3 0.2 0.2 0.1 Number with 0.1 Number with 0.0 earthquake 0.0 earthquake 0 1 2 3 4 0 1 2 3 4 insurance insurance (c) What is the most likely value for X?
Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 35% 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 that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.35)(0.65)(0.35)(0.35) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.) 1 2 3 4 P(x) (b) Draw the corresponding probability histogram. Probability 0.4 Probability 0.4 0.3 0.3 0.2 0.2 0.1 Number with 0.1 Number with 0.0 earthquake 0.0 earthquake 0 1 2 3 4 0 1 2 3 4 insurance insurance Probability Probability 0.4 0.4 0.3 0.3 0.2 0.2 0.1 Number with 0.1 Number with 0.0 earthquake 0.0 earthquake 0 1 2 3 4 0 1 2 3 4 insurance insurance (c) What is the most likely value for X?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 35% 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 that has insurance and F one who does not. Then one possible outcome is SFSS, with
probability (0.35)(0.65)(0.35)(0.35) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.)
1
2
3
4
p(x)
(b) Draw the corresponding probability histogram.
Probability
Probability
0.4t
0.4
0.3
0,3
0.2
0.2
0.1
Number with
0.1
Number with
0.0
earthquake
0.0
earthquake
0 1 2 3 4
0 1 2 3 4
insurance
insurance
Probability
Probability
0.4
0.4
0.3
0.3
0.2
0.2
0.1
Number with
0.1
Number with
0.0
earthquake
0.0
earthquake
0 1 2 3 4
0 1 2 3 4
insurance
insurance
(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? (Round your answer to four decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b0becd3-da7d-494c-b3c6-698d5c68dcd8%2F10098b9a-8460-4b0e-b404-2449ee9008ed%2Fj7zdx0c_processed.png&w=3840&q=75)
Transcribed Image Text:Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 35% 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 that has insurance and F one who does not. Then one possible outcome is SFSS, with
probability (0.35)(0.65)(0.35)(0.35) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.)
1
2
3
4
p(x)
(b) Draw the corresponding probability histogram.
Probability
Probability
0.4t
0.4
0.3
0,3
0.2
0.2
0.1
Number with
0.1
Number with
0.0
earthquake
0.0
earthquake
0 1 2 3 4
0 1 2 3 4
insurance
insurance
Probability
Probability
0.4
0.4
0.3
0.3
0.2
0.2
0.1
Number with
0.1
Number with
0.0
earthquake
0.0
earthquake
0 1 2 3 4
0 1 2 3 4
insurance
insurance
(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? (Round your answer to four decimal places.)
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