Assume that you have a riding lawn mower that is in need of repairs.You can choose to repair or replace it.You are interested in your net cost over the next two years.If you choose to repair,it will cost $300 and there is a 50/50 chance of whether or not it will need additional repairs within the next two years.If it does need additional repairs,there is a 40 percent chance of needing another $400 of repairs,and a 60 percent chance of needing another $200 of repairs.At the end of the two years you estimate that the repaired mower would be worthless. If you choose to replace the mower by trading in the old mower,the cost after deducting the trade in value is $1500.At the end of the two years you estimate there is a 75 percent chance you could resell it for $1000,and a 25 percent chance that you can resell it for $1300.
What is the expected value of repairing the mower?
A)A cost of $300
B)A cost of $400
C)A cost of $440
D)A cost of $290

Question

Quizplus · Accepted Answer

To find the expected value of repairing the mower, we need to calculate the total cost of repairs and the expected value of the mower at the end of two years.

If the mower does not need additional repairs, the total cost of repairs is $300 and the value of the mower at the end of two years is $0. Therefore, the expected value of this outcome is -$300.

If the mower needs an additional $400 of repairs, the total cost of repairs is $700 and the value of the mower at the end of two years is $0. Therefore, the expected value of this outcome is -$700.

If the mower needs an additional $200 of repairs, the total cost of repairs is $500 and the value of the mower at the end of two years is $0. Therefore, the expected value of this outcome is -$500.

To find the overall expected value of repairing the mower, we need to weigh the expected value of each outcome by its probability of occurring.

The probability of not needing additional repairs is 0.5, the probability of needing $400 of additional repairs is 0.2 (40% chance), and the probability of needing $200 of additional repairs is 0.3 (60% chance).

Therefore, the overall expected value of repairing the mower is:

(-$300 x 0.5) + (-$700 x 0.2) + (-$500 x 0.3) = -$440

This means that on average, repairing the mower will cost $440 over the next two years.

The best choice is to replace the mower, as the expected value of reselling it after two years is higher than the expected cost of repairing it. Therefore, the best choice is:

Answer: Replace the mower.

Assume That You Have a Riding Lawn Mower That Is