Question

A new fat-screen TV comes with a L-year warranty which completely covers any parts and repairsi At the end of the warranty period, the buyer is offered an eatended warranty for 3 moee years at a cost of $100. Industry tecords indicate that during that 3 year period, there's a 6% chance that a mingr repair averaging $95 wili be netded, and a 3.5% chance that a major repair averaging 5370 will be necded, Find the expected value of buying the extended warranty. The expected vatue of buying the extended warranty is:

Answer 1

The expected value of buying the extended warranty is $81.35.

Step-by-step explanation:

To find the expected value of buying the extended warranty, we need to calculate the cost of repairs during the 3-year period without the extended warranty, and compare it to the cost of repairs with the extended warranty.

1. Without the extended warranty:
   • The probability of a minor repair is 6%, with an average cost of $95. So the expected cost of a minor repair is 0.06 * $95 = $5.70.
   • The probability of a major repair is 3.5%, with an average cost of $370. So the expected cost of a major repair is 0.035 * $370 = $12.95.
   • Adding the expected cost of a minor and major repair gives us the expected cost of repairs without the extended warranty: $5.70 + $12.95 = $18.65.
2. With the extended warranty:
   • The cost of the extended warranty is $100.
   • Since the extended warranty completely covers any repairs, the expected cost of repairs with the extended warranty is $0.

To calculate the expected value of buying the extended warranty, we subtract the expected cost of repairs without the extended warranty from the cost of the extended warranty: $100 - $18.65 = $81.35.

Therefore, the expected value of buying the extended warranty is $81.35.