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okay this problem explains how to do this warranty problem okay the company estimates that point five percent thats not five percent thats point five percent and as a decimal thats point zero zero five right okay and the replacement cost is 350. so they want to know on average how much are they making every time i they say a warranty on average okay well all right so if it breaks down 0.005 of the time that means that 99.5 or 0.995 percent of the time or 0.995 as a proportion it does not fail so every time they sell a warranty theres a 99.5 chance that theyre not going to have any repercussions and theyre going to gain 19 dollars from it okay all right so that is okay now there is a chance 0.005 that it is going to fail and its going to cost them 350 but guess what they already paid 19 for that warranty so 350 minus 19 equals 331 okay all right so 0.995 times 19 because thats how much they get every time they sell a warranty and nothing happens minus this is the downside 0.005