A roulette wheel is divided into 38 pockets. 18 are numbered red pockets, 18 are numbered black pockets and 2 are green pockets. You can place bets on specific red or black pockets with odds of 35:1. That is, if you are correct you win $35 (plus the dollar you bet), and if you are incorrect, you lose the dollar you bet. A ball is spun into the wheel, and we will assume it lands in all pockets with equal probability. Your friend has developed what he describes as a "foolproof system" for winning. It involves him betting on $1 on 7 red again and again. You try to discourage him, but he is insistent. a. What are your friend's expected winnings after 1 spin of the wheel? What are his expected winnings after 36 spins of the wheel? b. Despite showing him the outcome of the above calculation, he is unwavering in his opinion, so you decide to at least try to make some money for yourself. You bet your friend $20 that at the end of 36 spins he will have lost money, i. e., have less money than he began with. What are your expected winnings in this bet? What are your friend's expected winnings after 36 spins taking this side-bet into account as well? Why is this? c. Now suppose that your friend plays for 26 spins. Should you make the bet with him now? What if he spins 30 times? 40 times? 70 times?