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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