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.

		Automobile Insurance
		Yes	No
Age	18 to 34	1500	340
	35 and over	1900	260

a. 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.

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

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

d.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.

e.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.

f.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.

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

Answer 1

	Automobile Insurance
		Yes	No
Age	18 to 34	1500	340
	35 and over	1900	260

Total number of drivers= 1500+340+1900+260=4000

Answer A:- A joint probability table will be formed as below:-

	Automobile Insurance
		Yes	No
Age	18 to 34	1500/4000 =0.375	340/4000=0.085
	35 and over	1900/4000=0.475	260/4000=0.065

	Automobile Insurance
		Yes (Y)	No (N)	Total
Age	18 to 34(A)	0.375	0.085	0.46
	35 and over (B)	0.475	0.065	0.54
	Total	0.85	0.15	1

In the above table

P(A) =0.46

P(B)=0.54

P(Y)=0.85

P(N)=0.15

Where,

(A)= age group of 18-34

(B) = 35 and above

(Y)= Those who have insurance

(N)= Those who do not have insurance

Answer B:- In the table of question A, P(A)=0.46 while P(B)=0.54

This will indicate that in the population of the USA, the people of age grip 18-3 are 46%, while the population of 35 years or more is 54%.

Answer C:- the probability that a randomly selected individual does not have automobile insurance coverage is represented as P(N) which is equal to 0.15 thus the answer is 0.15.

Answer D:- If the individual is between the ages of 18 and 34, the probability that the individual does not have automobile insurance coverage is represented by 340/4000=0.085

So the answer is”= 0.085

Answer E:- If the individual is age 35 or over, the probability that the individual does not have automobile insurance coverage is 260/4000=0.065

So the answer is:- 0.065

Answer F:- If the individual does not have automobile insurance, the probability that the individual is in the 18-34 age group is 340/(340+260) =0.57

So that answer is:- 0.567

Answer G:- The probability information indicates that the probability of young drivers to have the insurance is quite less in comparison to the drivers falling in the age group of 35 years and more.