2. Jim has a 5-year old car in reasonably good condition. He wants to take out a $40,000 term (that is accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having and accident in theyear in which it is x years old is as follow:

x=age
5
6
7
8
9
P(accident)
0.01191
0.01292
0.01396
0.01503
0.01613
Please show work
thank you

To calculate the cost of the insurance policy, we need to calculate the probability of having an accident each year from the age of 5 to the age of 10, and then multiply it by the coverage amount ($40,000).

First, let's calculate the probability of having an accident each year:

Year 5: P(accident) = 0.01191
Year 6: P(accident) = 0.01292
Year 7: P(accident) = 0.01396
Year 8: P(accident) = 0.01503
Year 9: P(accident) = 0.01613

Now, let's calculate the total cost of the insurance policy by summing up the product of the probability of an accident and the coverage amount ($40,000) for each year:

Cost of insurance policy = (Year 5 probability) * $40,000 + (Year 6 probability) * $40,000 + (Year 7 probability) * $40,000 + (Year 8 probability) * $40,000 + (Year 9 probability) * $40,000

= 0.01191 * $40,000 + 0.01292 * $40,000 + 0.01396 * $40,000 + 0.01503 * $40,000 + 0.01613 * $40,000

= $476.40 + $516.80 + $558.40 + $601.20 + $645.20

= $2,797.00

Therefore, the cost of the insurance policy for Jim's 5-year-old car until it is 10 years old would be $2,797.00.

To determine the cost of the car insurance policy, we need to calculate the expected value of the accident benefit for each year until the car is 10 years old.

The expected value of an accident benefit is calculated by multiplying the probability of an accident occurring in a given year by the amount of the benefit. In this case, the benefit amount is $40,000.

Let's calculate the expected value for each year:

Year 5:
Expected Value = Probability of Accident * Benefit Amount
Expected Value = 0.01191 * $40,000 = $476.40

Year 6:
Expected Value = 0.01292 * $40,000 = $516.80

Year 7:
Expected Value = 0.01396 * $40,000 = $558.40

Year 8:
Expected Value = 0.01503 * $40,000 = $601.20

Year 9:
Expected Value = 0.01613 * $40,000 = $645.20

Now that we have calculated the expected value for each year, we can sum them up to find the total expected value for the policy:

Total Expected Value = $476.40 + $516.80 + $558.40 + $601.20 + $645.20
Total Expected Value = $2,798

Therefore, the expected cost of the car insurance policy would be $2,798.