Question

An automobile insurance company is in the process of reviewing its policies. The company is considering increasing the premium charged to drivers under 25. According to company records, 35 percent of the insured drivers are under the age of 25. Company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident. On the other hand, only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident.
An accident has just been reported.

1. What is the probability that the insured driver is under the age of 25?
2. What is the probability that an insured driver of any age will be involved in an accident?

Answer 1

(a)

From the given data, the following Table is calculated:

	Under age of 25	Over age of 25	Total
Involved in at least one automobile accident	280	130	410
No accident	700 - 280 = 420	1300 - 130 = 1170	1590
Total	2000 X 0.35 = 700	2000 - 700 = 1300	2000

P(Under age 25/ Accident) = P(Under age 25 AND Accident)/ P(Accident) = 280/410 = 0.6829

So,

Answer is:

0.6829

(a)

From the given data, the following Table is calculated:

	Under age of 25	Over age of 25	Total
Involved in at least one automobile accident	280	130	410
No accident	700 - 280 = 420	1300 - 130 = 1170	1590
Total	2000 X 0.35 = 700	2000 - 700 = 1300	2000

P(Under age 25/ Accident) = P(Any age AND Accident)/ P(Accident) = 410/410 = 1.00

So,

Answer is:

1.00