European roulette. The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money.
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
(c) How do your answers to parts (a) and (b) compare? What does this say about the riskiness of the two games?