# SOLUTION: Please help, I'm gettin no where with it. Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for

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 Question 175401: Please help, I'm gettin no where with it. Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of \$16,000 on the certain type of car?Answer by stanbon(57967)   (Show Source): You can put this solution on YOUR website!Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of \$16,000 on the certain type of car? ---------------- That is an "expected value" problem. The random variable is "cost to the car owner". Cost is -x if his car is not stolen or (16000-x) if it is stolen The probability of -x is (399/400); the prob of (16000-x) is (1/400) -------------------- The expected value is (399/400)(-x) + (1/400)(16000-x) ---------------------- For the owner to "break even" this expected value should be zero. (399/400)(-x) + (1/400)(16000-x) = 0 -399x + 16000-x = 0 -400x = -16000 x = \$40.00 (His annual cost should be \$40). ============================ Cheers, Stan H.