The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range. Compute the probability of winning the following types of bets: Betting on two numbers that touch each other on the table, as in 10-11 or 10-13 Betting on 0-00-1-2-3 Betting on 0-1-2; or 0-00-2; or 00-2-3

The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range. Compute the probability of winning the following types of bets: Betting on two numbers that touch each other on the table, as in 10-11 or 10-13 Betting on 0-00-1-2-3 Betting on 0-1-2; or 0-00-2; or 00-2-3

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In the gambling game "craps", a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up sides of the six-sided dice. The bettor wins on the first roll if the sum is 7 or 11. The bettor loses on the first roll if the sum is 2,3, or 12. If the sum is 4,5,6,8,9, or 10, that number is called the bettor's "point". Once the point is established, the rule is as follows: If the bettor rolls a 7 before the point, the bettor loses; but if the point is rolled before a 7, the bettor wins. (a)List the 36 outcomes in the sample space for the roll of a pair of dice. Assume that each of them has a probability of 1/36. (b)Find the probability that the bettor wins on the first roll. That is, find the probability of rolling a 7 or 11, P(7 or 11).
When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Assume a single spin of the roulette wheel is made. Find the probability of winning with the given bet. An example of a line bet is betting that the marble will land in a slot numbered 14, 15, 16, 17, 18, or 19. The probability of winning with the given line bet is (Type an integer or a simplified fraction.)
In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet $8 on red. If the ball lands on red, you get to keep the $8 you paid to play the game, and you are awarded $9. If the ball lands elsewhere, you are awarded nothing, and the $8 that you bet is collected. What is the expected value of the game?
When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Assume a single spin of the roulette wheel is made. Find the probability of winning with the given bet. An example of a lineline bet is betting that the marble will land in a slot numbered 3, 4, 5, 6, 7, or 8 The probability of winning with the given line bet is
XYZ company has designed a new lottery scratch-off game. The player is instructed to scratch off one spot: A, B, or C. A can reveal "loser," "win $1," or "win $50." B can reveal "loser" or "take a second chance." C can reveal "loser," or "win $500." On the second chance, the player is instructed to scratch off D or E. D can reveal "loser" or "win $1." E can reveal "loser" or "win $10." The probabilities at A are 0.9, 0.09, and 0.01 respectively. The probabilities at B are 0.8 and 0.2. The probabilities at Care 0.999 and 0.001. The probabilities at D are 0.95 and 0.05. The probabilities at E are 0.5 and 0.5. Calculate the expected value of the game and provide recommendations to a decision-maker
Many casinos have a game called the Big Six Money Wheel, which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts, as shown in the table at the top of the next column. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player's bet, the player wins that amount for each dollar bet. Denomination Number of slots $40 (Joker) 1 $40 (Casino logo) 1 $20 2 $10 4 $5 7 $2 15 $1 24 If a player bets $4 on the $10 denomination, find the player's expectation. (Round your answer to two decimal places.)
Are the casinos really gambling when we place a bet against them? Explain
Laura has a bag with 8 balls numbered 1 through 8. She is playing a game of chance. This game is this: Laura chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. She loses $14 if 7 or 8 is selected. (a) Find the expected value of playing the game. dollars (b) What can Laura expect in the long run, after playing the game many times? (She replaces the ball in the bag each time.) O Laura can expect to gain money. She can expect to win dollars per selection. O Laura can expect to lose money. She can expect to lose dollars per selection. O Laura can expect to break even (neither gain nor lose money). X
You are going to roll three standard six sided dice. The dice are distinguishable: one is red, and other is blue, and the third is yellow. How many different roles are there?
James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or…