Use this information for problems 1 and 2. You play a game with a friend where you roll a 6- sided die. 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. 2. You win $4 if the die roll is larger than 4 and pay your friend $1 if it isn't. 3. 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 $2. If you get a blue stone, you win nothing. What is the expected value for you? Use this information for problems 4-6. You buy a scratcher lottery ticket for $3. You 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? 6. 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? 7. 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? 8. 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