284 Unit 3 Place Your Bets Did You Get It 5. If seven cards are numbered with integers from -2 to 4, then placed into a box and picked out at random, find the expected value. dove no seol to thaw blew While gambling games are the typical go-to examples for computing expected value, they're not by any means the only appli- cation. Let's look at the world of automobile insurance. If you think of it, buying insurance is kind of like gambling: You're betting that something bad will happen to your car. If nothing happens, you've paid the insurance company for nothing. But if something does happen, when they pay for repairs, you're basically "winning" the bet. Suppose that a driver named Karl pays $800 per year on insurance for his SUV. According to insurance industry stats I found online, the average motorist has a 5.6% chance of getting in an accident in any given year, and the average collision claim paid by insurance companies is $3,160. Our goal will be to find the expected value if Karl buys 1 year's worth of car insurance. 16. If Karl does get in an accident and his insurance company pays the average claim, what is Karl's net gain? Don't forget the amount he paid for insurance. 17. If Karl remains accident-free for the year, what is his net loss? 18. Fill in the probability distribution, and use it to find Karl's expected value. Result Outcome (Gain or Loss) Probability Accident No accident why mobius & bollso et , aib s an pubavibas sno mort yinrob 19. Based on the expected value you calculated, is Karl paying too much for car insurance? Explain