1. A roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers chooses red or black. A bet of $1 on red returns $2 if the ball lands in a red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. (a) What is the expected gain on a $1 bet on red? (b) One way to think of the expected value in this case is that it is the "mean loss/gain per bet". Explain what the law of large numbers tells us about what will happen if a gambler makes many bets on red. [2, 10.19]