I cant seem to get how to get these answers

Question

An LG Dishwasher, which costs $750, has a 15% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. Assume the dishwasher is replaced in the first 2 years.

a) Write out the probability distribution for the value of the extended warranty.

   Make sure you enter your X values from smallest to largest.

X	P(X)

b) What is the expected value of the extended warranty?

  Round final answer to 2 decimal places and write the units in the second box.

Answer 1

Well if the dishwasher needs to be replaced the value is (750 - 112.10) = 637.90, because the dishwasher is replaced for a payment of 112.10, saving 637.90

If the dishwasher isnt replaced value is -112.10, because you pay out 112.10 with no benefit

so

X probability

0.15 637.90

0.85 - 112.10

expected value of X is 0.15 x 637.90 + 0.85 ( -112.10) = $ 0.40

[ so if N is a large number > 10000, if N dishwashers are bought the total benefit of the warranty to the owners will be approx $ 0.40 N]