Question

The following table provides the expected repair cost of a laptop and respective probabilities (likelihood) for 5 years after purchase.

Type of Repair	Probability	Repair Cost
None	0.80	$0
Minor	0.10	$100
Major	0.08	$400
Catastrophic	.02	$1000

What is the probability of any failure that require repair in the next 5 years? What is the expected repair cost? What is the Standard deviation of repair cost? Hint: Use Excel. If the cost of purchasing a 5-year warranty is $99, calculate the expected gain or loss for a consumer that purchase this warranty. Would you recommend purchasing a warranty? Why? Would you a buy 5-year warranty if it costs $59.95?

Answer 1

The probability of any failure that require repair in the next 5 years = 0.10+0.08+0.02 = 0.2

The expected repair cost = 0.80$0 + 0.10$100 + 0.08$400 + 0.02$1000 = $62

The variance of repair cost = 0.80($0)² + 0.10($100)² + 0.08($400)² + 0.02($1000)² - ($62)² = $²33800

The standard deviation of repair cost = $ $183.848

If the cost of purchasing a 5-year warranty is $99, the expected loss for a consumer that purchase this warranty

= $99 - $62 = $37

So one would not recommend purchasing a warranty as a loss of $37 is expected.

But one would buy 5-year warranty if it costs $59.95, less than than the expected repair cost in the next 5 years. A gain of $62 - $59.95 = $2.05 is expected on buying the warranty for $59.95.