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 dierent 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?