A company estimates that 0.6% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400.

If they offer a 2 year extended warranty for $26, what is the company's expected value of each warranty sold?

Question

A company estimates that 0.6% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400.

If they offer a 2 year extended warranty for $26, what is the company's expected value of each warranty sold?

anonymous · Answer

Your expected value is a weighted average given by $$E[X] = p_{1}x_{1} + ... + p_{n}x_{n}$$

In this problem, if you're working for the company, you have a 0.06% = .0006 probably that you will have to spend $400, and a 1-.0006 = .9994 probability that you instead will make $26 for selling the warranty. Plugging these values in, we get
$$p_{1} = .0006$$$$x_{1} = -400$$$$p_{2} = .9994$$$$x_{2} = 26$$
$$E[X] = (.0006)(-400) + (.9994)(26) = 25.7444$$