Michael T. answered • 11/19/19

Outstanding former math student passionate to share knowledge

First, you must interpret that 0.9% is the probability that the extended warranty has to cover a replacement cost. To help understand this, imagine that the original warranty is only 1 year long. The question is then saying that 0.9% is the probability that a product will not fail for the 1st year and then fail in the 2nd year. Thus, it is the probability that the extended warranty has to cover a replacement cost.

Then, just work the math. The expected value of the warranty to the company is the $45 it receives for the warranty minus the expected value of the replacement cost, which is 0.009 * $300. So, the answer is:

$45 - (0.009 * $300) = $42.30

Hope this helps!