Question

"Suppose the warranty period on your family’s new television is about to expire and you are debating about whether to buy a one-year maintenance contract for $35. If you buy the contract, all repairs for one year are free. Consumer information shows that 12% of the televisions like yours require an annual repair that costs $140 on the average. What is the expected value of buying the maintenance contract?"

Answer 1

The expected value of buying the maintenance contract is -$51.80, indicating that, on average, buying the contract would result in a loss.

Step-by-step explanation:

To calculate the expected value of buying the maintenance contract, we need to consider the cost of repairs with and without the contract. Without the contract, there is a 12% chance of needing a $140 repair, so the expected cost without the contract is 12% * $140 = $16.80. With the contract, all repairs are free, so the expected cost with the contract is $0.

The cost of the maintenance contract is $35. Therefore, the expected value of buying the maintenance contract is:

Expected value = $0 (cost with contract) - $16.80 (cost without contract) - $35 (cost of contract) = -$51.80

Since the expected value is negative, it means that, on average, buying the maintenance contract would result in a loss. Therefore, it may not be a wise decision to buy the maintenance contract.