During a recent period of high unemployment, hundreds of thousands of drivers dr

Question

During a recent period of high unemployment, hundreds of thousands of drivers dropped their automobile insurance. Sample data representative of the national automobile insurance coverage for individuals 18 years of age and older are shown here.

Develop a joint probability table for these data and use the table to answer the remaining questions. If required, round your answers to three decimal places.

What do the marginal probabilities tell you about the age of the U.S. population?

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What is the probability that a randomly selected individual does not have automobile insurance coverage? If required, round your answer to three decimal places.

If the individual is between the ages of 18 and 34, what is the probability that the individual does not have automobile insurance coverage? If required, round your answer to three decimal places.

If the individual is age 35 or over, what is the probability that the individual does not have automobile insurance coverage? If required, round your answer to three decimal places.

If the individual does not have automobile insurance, what is the probability that the individual is in the 18-34 age group? If required, round your answer to three decimal places.

What does the probability information tell you about automobile insurance coverage in the United States?

Automobile Insurance Yes No Age 18 to 34 1600 340 35 and over 1900 240

Explanation / Answer

Lets first construct the belwo table to answer the below 4 subparts of the question

What is the probability that a randomly selected individual does not have automobile insurance coverage? If required, round your answer to three decimal places.

Total number of people = 4080 , number of people with no auto insurance = 580 ,

so the probability is 580/4080 = 0.142

If the individual is between the ages of 18 and 34, what is the probability that the individual does not have automobile insurance coverage? If required, round your answer to three decimal places.

Number of people in the age group 18-34 = 1940 , numer of people who dont have insurance within the group = 340

so the required probability is 340/1940 = 0.175

If the individual is age 35 or over, what is the probability that the individual does not have automobile insurance coverage? If required, round your answer to three decimal places.

Number of people in 35 age group = 2140 , and people not having insurance in this group = 240

so the required probability is 240/2140 = 0.112

If the individual does not have automobile insurance, what is the probability that the individual is in the 18-34 age group? If required, round your answer to three decimal places.

total number of people who dontr have auto insurance = 580 , number of people who are in age 18-34 and dont have insurance = 340

340/580 = 0.586

Hope this helps !! Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

Automobile Insurance Yes No Totals Age 18 to 34 1600 340 1940 35 and over 1900 240 2140 Totals 3500 580 4080

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