Ex. 2.40 European roulette.

The game of European roulette involves spinning a wheel with 37slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheeland will eventually land in a slot, where each slot has an equalchance of capturing the ball. Gamblers can place bets on red orblack. If the ball lands on their colour, they double their money.If it lands on another colour, they lose their money.

(a) Suppose you play roulette and bet $3 on a single round. Whatis the expected value and standard deviation of your totalwinnings?

(b) Suppose you bet $1 in three different rounds. What is theexpected value and standard deviation of your total winnings?

(c) How do your answers to parts (a) and (b) compare? What doesthis say about the riskiness of the two games?

Ex. 2.34 Ace of clubs wins.

Consider the following card game with a well-shuffled deck ofcards. If you draw a red card, you win nothing. If you get a spade,you win $5. For any club, you win $10 plus an extra $20 for the aceof clubs.

(a) Create a probability model for the amount you win at thisgame. Also, find the expected winnings for a single game and thestandard deviation of the winnings.

(b) What is the maximum amount you would be willing to pay toplay this game? Explain your reasoning.