Use this information for problems 9 and 10. A loan is also a similar kind of "game.\" A bank loans you $100 to pay back in 1 year, plus 18% interest - so you will pay back $118. The bank computes that there is a 0.3% chance that you fail to pay back the loan. 9. If you pay back the loan, how much money does the bank "win" (how much more money will they have than they did before they made the loan)? If you don't pay back the loan, how much money does the bank "lose\"? 10' what is the expected value ofthe loan for the bank? Homework 4.3: Expected Value Vou should complete the homework assignment by the due date on Blackboard. Failure to submit the homework by 11:59 PM on the due date will result in a zero on the assignment. Remember that copying another student's assignment, having someone else complete your assignment, or downloading answers from online are all academic misconduct and will result in a 0 on the assignment. You MAY work together with other students, but you should submit all of your own work. You should show all work on every problem failure to do so may result in zero credit on the problem Use this information for problems 1 and 2. You play a game with a friend where you roll a 6- sided dle. Find the expected value for you in each case: 1. You win $2 if the die roll is an even number and pay your friend $3 if the die roll is an odd number. . You win $4 if the die roll is larger than 4 and pay your friend $1 if it isn't. . You play a game with a friend where you pay $1 to play. You reach into a bag containing 6 red stones and 14 blue stones. If you draw out a red stone, you win 52. If you get a blue stone, you win nothing. What is the expected value for you? Use this information for problems 4-6. Vou buy a scratcher lottery ticket for $3. Vou have a 1% chance of winning $10, and a 0.001% chance of winning $1000. 4. What is the probability that you don't win either prize? 5. What is the expected value of playing the game? . A friend tells you that they're going to buy 100 scratcher lottery tickets, so that they're guaranteed to win. Why doesn't this make sense? How much money should your friend expect to lose overall on 100 tickets? . An insurance company charges $1200 a year for automobile insurance. They estimate that there is a 1% chance that you have an accident each year, and that they would have to pay $4000 in damages for that accident. What is the expected value for the insurance company? . An insurance company charges $2500 each year for home insurance. They estimate that there is a 0.01% chance that you will have an incident that costs them $10,000, and a 0.0001% chance that you have an incident that costs them $50,000. What is the expected value for the insurance company