A man is considering buying a one-year warranty for $100, which will cover the $600 replacement cost for his new swimming pool pump. The probability the pump does not break within the first year is 90%. A) The expected value is −$90, so the man should not buy the warranty. B) The expected value is $90, so the man should buy the warranty. C) The expected value is −$40, so the man should not buy the warranty. D) The expected value is $40, so the man should buy the warranty.It'd help me out a lot if you explained your answer!

Answer:C) The expected value is −$40, so the man should not buy the warranty. Step-by-step explanation:The expected value is( each value times the respective probability) minus the cost of the itemE = cost * probability + no cost * probability    It will cost 600 dollars if it breaks * 10 percent chance it breaks    It will cost nothing if it does not break * 90 percent chance it does not breakE = 600 * .1 + 0*90E = 60 +0E = 60Now we subtract the 100 dollars for the warrantyE - 10060-100-40Our expected cost is -40