Question

# A company estimates that 8% of their products will fail after the original warranty period but...

A company estimates that 8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of \$100. If they want to offer a 2 year extended warranty, what price should they charge so that they'll break even (in other words, so the expected value will be 0) \$______

We are asked, if they want to offer 2 years extended warranty, what price should they charge.

Suppose this prize = x.

So, we need to find the value of x.

The probability of outcomes are, 1 - 0.08 = 0.92 and 0.08 respectively.

 Prize Probability 100 0.08 100 - x 0.92

And expected value = 0

That is ,

100*0.08 + (100 - x)*0.92 = 0

8 + (92 - 0.92*x) = 0

100 - 0.92*x = 0

0.92*x = 100

x = 100/0.92

x = 108.6957

That is, if they want to offer 2 years extended warranty, then the price should = \$108.6957

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