% do DII F5 (3) The game of roulette consists of a small ball and a wheel with 38 numbered pockets around the edge: the numbers 1 through 36, and two copies of 0 (the second zero is labelled "00"). Some other important information: • 18 numbers are red: 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, and 36 • 18 numbers are black: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, and 35 • The numbers 0 and 00 are green You bet by placing your chips on a felt table, with a 12 by 3 grid of the 36 numbers, and side places for some special bets (including betting on 0 or 00). You win your bet if the ball lands on a number that satisfies the conditions of your bet. If you lose, you don't get any money. If you win your bet, your payout is your money back, PLUS your bet times the odds given according to the table below: Bet Name Straight Up bet Split bet A single number Odds (for payout) What You're Betting On 35 to 1 Dozens bet Low/High bet Red/Black bet Two numbers adjacent to each other on the table The 1st dozen (1-12), 2nd dozen (13-24), or 3rd (25-36) The numbers 1 through 18 or 19 through 36 The red/black numbers 17 to 1 2 to 1 1 to 1 1 to 1 So, for example, if you bet $1 on a straight up bet on 13, and the ball lands on 13, your payout would be $36, which is your dollar back plus 35 times your bet. Note: This is NOT a complete list! But it's enough for the homework. Note 2: "Odds" in roulette do not quite match the actual probabilities of success for the respective bets. They are just for determining payout (a common practice in gambling). Suppose you make a $10 bet on the second dozen (13 through 24). What is your expected payout? (a) (b) (c) (d): Suppose you make a $5 bet on the number 17 straight up (James Bond's favorite roulette bet). What is your expected payout? In roulette, you are allowed to make multiple bets in a single spin. Suppose you make both bets from Parts A and B simultaneously. What is your expected payout? Why do you think the casino sets their payouts according to the odds offered? Q Search O: F6 ※ & F7 PrtScn AF8 Home End PgUp F9 PgDn F10 F11 F12 6/2