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 that has insurance and Fone who does not. Then one possible outcome is SFSS, with probability (0.25)(0.75)(0.25)(0.25) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.) 2 P(x) (b) Draw the corresponding probability histogram. 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 Probability Probability 0.4 04 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 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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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 that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.25)(0.75)(0.25)(0.25) and associated X value 3. There are 15 other outcomes.] (Round
your answers to four decimal places.)
p(x)
(b) Draw the corresponding probability histogram.
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
2
3
4
1
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
1.
3
4
1
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.)
Transcribed Image Text: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 that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.25)(0.75)(0.25)(0.25) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.) p(x) (b) Draw the corresponding probability histogram. 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 2 3 4 1 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 1. 3 4 1 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.)
Expert Solution
Step 1

Probability is the chances of occurrence of an event. The value of probability lies between 0 and 1. If the probability is 0 then the event will not occur and if the value is 1 then the event will occur.

The probability is the ratio of number of favourable outcomes to total number of possible outcomes. If two events are independent then probability that both the events occur together is equal to multiplication of probability of each event.

PAB=PA·PB

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