Question

In: Statistics and Probability

ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into...

ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into a location marked by one particular colored number. In the United States there are 18 locations colored red, 18 locations colored black and 2 locations colored green. The red and black locations are numbered 1-36 and the green locations are labeled "0" and "00" as shown in the picture to the right. The wheel therefore has 38 locations in total. Note that the odd and even values are not evenly distributed within each color.

For any particular wager a player makes, an expected profit can be calculated from: Expected profit = (Prob. of winning) x (winning payout amount) - wager

(a) One potential wager is to "bet on black" where you make a wager and if the ball lands in a black location you win an additional amount equal to the wager for a total payout equal to twice the wager. For example, if you bet $1 and win the casino gives you a $2 payout. If the ball lands on red or green you would lose your wager and the payout would be $0. What is the expected profit from making a $13 "bet on black"? (round to closest penny)

(b) To “let it ride” is to make a bet and if it wins to make the same bet with the entire payout amount. For example, if you bet $1 on black and win the casino gives you $2, you then "let it ride" by betting that $2 on black and if you win again the casino would give you $4. If the ball were to land on red or green on either spin of the wheel you would lose your wager and the final payout would be $0. What is the expected profit for betting $15 on black and if you win, "letting it ride" once? I.E., betting on black and if you win betting your winnings on black again? (keep in mind that if you lose the first bet you are done; round to closest penny)

(c) Another potential wager is to "bet on odd" which has the same payout as betting on black, but wins only when the ball lands in a location with an odd number of either color. If the ball lands on an even numbered location or a green space you lose your wager and the payout would be $0. What is the expected profit from placing two bets on a single spin - $17 on black and $19 on odd? (round to closest penny)

Solutions

Expert Solution


Related Solutions

ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into...
ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into a location marked by one particular colored number. In the United States there are 18 locations colored red, 18 locations colored black and 2 locations colored green. The red and black locations are numbered 1-36 and the green locations are labeled "0" and "00" as shown in the picture to the right. The wheel therefore has 38 locations in total. Note that the odd...
ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into...
ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into a location marked by one particular colored number. In the United States there are 18 locations colored red, 18 locations colored black and 2 locations colored green. The red and black locations are numbered 1-36 and the green locations are labeled "0" and "00" as shown in the picture to the right. The wheel therefore has 38 locations in total. Note that the odd...
ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into...
ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into a location marked by one particular colored number. In the United States there are 18 locations colored red, 18 locations colored black and 2 locations colored green. The red and black locations are numbered 1-36 and the green locations are labeled "0" and "00" as shown in the picture to the right. The wheel therefore has 38 locations in total. Note that the odd...
Roulette is a casino game that involves spinning a ball on a wheel that is marked...
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1-36 are red and half are black, 0 and 00 are green. Each number occurs only once on the wheel. The most common bets are to bet on a single number or to bet on a color (red or black). The pocket in which the ball lands on the wheel determines...
Roulette is a casino game that involves spinning a ball on a wheel that is marked...
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black or green. Half of the numbers 1-36 are colored red and half are black. The numbers 0 and 00 are green. Each number occurs only once on the wheel. We can make many different types of bets but the simplest are to bet on a number or on a color (either red or black). These are the...
STRAIGHT FROM THE BOOK Roulette In the casino game of roulette there is a wheel with...
STRAIGHT FROM THE BOOK Roulette In the casino game of roulette there is a wheel with 19 black slots, 19 red slots, and 2 green slots. In the game, a ball is rolled around a spinning wheel and it lands in one of the slots. It is assumed that each slot has the same probability of getting the ball. This results in the table of probabilities below. Fair Table Probabilities   black     red     green   Probability   19/40 19/40 2/40 You watch the...
In the game of roulette, a steel ball is rolled onto a wheel that contains 18...
In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 38 times, find the probability of the following events. A. The ball falls into the green slots 3 or more times. Probability = (0.3815 is the wrong answer) B. The ball does not fall into any green slots. Probability = (0.2590 is wrong) C. The ball falls into black slots 14 or...
In the game of roulette, a steel ball is rolled onto a wheel that contains 18...
In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 38 times, find the probability of the following events. A. The ball falls into the green slots 4 or more times. B. The ball does not fall into any green slots. C. The ball falls into black slots 15 or more times. D. The ball falls into red slots 10 or fewer...
In the game of roulette, there is a wheel with 37 slots numbered with the integers...
In the game of roulette, there is a wheel with 37 slots numbered with the integers from 0 to 36, inclusive. A player bets $3 and chooses a number. The wheel is spun and a ball rolls on the wheel. If the ball lands in the slot showing the chosen number, the player receives $3 plus 100$. Otherwise, the player loses the $3 bet. Assume that all numbers are equally likely. Determine the variance of the gain or loss per...
In the popular American game of roulette, the roulette wheel has 38 spaces that are numbered...
In the popular American game of roulette, the roulette wheel has 38 spaces that are numbered 0, 00, and 1 through 36, 0. Find the probability of getting the following: a) A number that is less than 15, not counting 0 and 00; b) A number that is a multiple of 3 or 5, not counting 0 and 00; c) An odd number that is less than 15, not counting 0 and 00; d) A number that is between 1...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT