1. Someone offers you a game of unbiased coin toss, where you win 111 USD on tails, and lose 85 USD on heads. What is the expected value of one such toss?
2. Someone offers you a game of unbiased die roll, where you win 96 USD on 1, and lose 12 USD on anything other than 1. What is the expected value of one roll?
3. Someone offers you a game of 100 fair-coin tosses, where you win 10 USD on tails, and lose 155 USD on heads. What is the minimum number of rounds that you must win out of 100, in order to avoid a net loss?
4. On a roll of a 10-sided die, with faces numbered as integers 1 through 10, you're offered a payout of 4.5 bucks times the number on the face that comes up. What is the expected value of this roll?
5. You are to roll two regular six-sided dice. If the sum of he values is 6, you are to receive 42 USD. What is the expected value of this proposition?