please help me answer this question , thanks !

In this activity, we'll be exploring the casino game: roulette. Work through the following problems carefully, and you'll become an expert on this game played throughout the world. European American Single and Double 0 You should know by now that there are two different styles of wheel: European (contains 0) and American (contains 0 and 00). Below is a payoff table (From Wikipedia) of some of the most popular bets in roulette. Note that the payouts are the same regardless of whether you're playing the European wheel or American wheel. Note these are the payouts and NOT the odds of winning. High 19, 20I 21, ..., 36 1 to 1 Any single number any three numbers horizontal (1, 2, 3 or 4, 5, 6, etc.) any four adjoining numbers in a block come' (1, 2, 4, 5 or 17, 18. 8 to 1 20, 21, etc.) \fLet's calculate the expected payoffs of a couple popular bets on these wheels. In many casinos, the lowest table you'll be able to nd is a $10 dollar minimum (if you're lucky, you can nd $5 tables). Suppose you make a $10 bet on \"Even" on a European wheel. What is your expected payout? Let's use the convention that we consider out payouts as losing = -1*Bet and winning is Bet\" Payout Pr(Even) = 18/37, Pr(Not Even) = 19/37. 50 E(Even Bet) = Pr(Even) * Bet * Payout + Pr(Not Even) * -1 * Bet = 18/37 * 10 + 19/37 * (-10) = -10/37 Suppose you make a $10 bet on \"Odd\" on an American wheel. What is your expected payout? Pr(Odd) = 13/33, Pr(Not Odd) = 20/33. 50 E(Odd Bet) = 13/33 * 10 + 20/33 * (-10) = -20/33 Suppose you make a $10 bet on \"12\" on a European wheel. What is your expected payout? Pr(12) = 1/37, Pr(Not 12) = 36/37. So El12) = 1/37 * 35 * 10 + 36/37 "' (-10) = -10/37 Suppose you make a $10 bet on \"3\" on an American wheel. What is your expected payout? Pr(3) = 1/33, Pr(Not 3) = 37/33. So 5(3) = 1/33 * 1o * 35 + 36/38 * (-10) = -20/33 Another rule that is played at some European casinos (although rare) is the en prison rule. This rule states that if the roulette wheel selects the number 0, any bet on odds/evens, red/black, or low/high will result in the player having the option of placing their entire bet in prison. The wheel is then spun again and if the wheel hits their original bet, their original wager is returned to them (if 0 comes up again, the bet is lost). 10. Suppose you bet $10 on black, what is the expected payout if the "en prison" rule is in effect