26. The game of craps is played as follows: A player rollstwo dice. If the sum of the dice is either a 2, 3, or 12, theplayer loses; if the sum is either a 7 or an 11, the playerwins. If the outcome is anything else, the player continuesto roll the dice until she rolls either the initial outcome or a7. If the 7 comes first, the player loses, whereas if the initialoutcome reoccurs before the 7 appears, the player wins.Compute the probability of a player winning at craps.Hint: Let E; denote the event that the initial outcome is12i=2i and the player wins. The desired probability is P(E;).To compute P(E;), define the events Ein to be the eventthat the initial sum is i and the player wins on the nth roll.∞Argue that P(E₁) = P(Ein).n=1

Given the conditions to play the game of craps: A player rolls two dice.If the sum of the dice is…

Answered: 26. The game of craps is played as…

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...

See similar textbooks

Similar questions

the carnival has come to town, and lucky louie has once again set up his pavilion. He offers a simple game consisting of rolling two normal six-sided dice at the same time for the extraordinarily low price of $3.00 per play. If the player rolls a sum of 3, the player wins $13.00; if the sum is a 9, the player wins $9.00; and if the sum is a 12, the player wins $12.00. Otherwise, the player does not win anything. How much should you expect to win or lose per game (after paying the $3.00) ?
Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
A pair of fair dice is rolled onoe, Suppose that you lose $7 if the dice sum to 5 and win $8 if the dice sum to 11 or 12. How much should you win or lose if any other number tums up in order for the game to be fair? To keep the game fair, you should (Do not round until the final answer. Then round to the nearest cent as needed.) if the dice sum to any other number
Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once. (i) How many ways can you roll all the dice? (ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points? (iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this? (iv) Suppose instead you are trying to get your dice to roll 4 consecutive numbers (ex. (1, 2, 3, 4, 1) or (2, 3, 4, 5, 3)) How many different ways are there to do this? (make sure to not count any only consecutive numbers) This is a combinatorics math counting problem.
A vending machine contains 1000 lollipops. Some of the lollipops are red, and the others are blue. You don’t know how many there are of each color. However, you do know that these two alternatives are equally likely. There are 900 blue lollipops and 100 red ones. There are 500 blue lollipops and 500 red ones. When you put a coin into the vending machine, it gives you a lollipop, chosen at random. Suppose that it gives you a blue lollipop. What is the probability that there are 900 blue lollipops and 100 red ones? Show how you got the answer.
In a gambling game, I roll two dice and win $1 if the sum of my two rolls is largerthan 7. I lose $1 if the sum of my two rolls is smaller than 7. In any other cases, Idon’t lose or win anything. I am going to repeat this game 72 times. c) Now make a box model for the number of times I win, including the values onthe tickets, the number of repeats of each ticket, and how many draws we willmake with replacement from the box. The average of the tickets in the box from (c) is ___________ and the SD is___________.
Y Ou are piaying a game involving a fair 6-sided die and a fair coin. First the die is rolled. If the number on the die is evenly divisible by 3 (i.e., either 3 or 6), then the coin is flipped twice, but if the number on the die is not evenly divisible by 3 (i.e., either 1, 2, 4 or 5), then the coin is flipped only once. You win $1 every time head appears on the coin and you win nothing every time a tail appears. а.) b.) did win some money. On one play of the game, determine the probability that you win some money. Determine the probability that the roll of the die was a 3 or a 6, given that you
In a game, two coins are tossed. If either of the coins comes up heads, you have won a prize. To claim the prize, you must point to one of your coins that is a head and say 'look, that coin's a head, I've won'. You watch Fred play the game. He tosses the two coins, and he points to a coin and says 'look, that coin's a head, I've won'. What is the probability that the other coin is a head?
A certain game involves tossing 3 fair coins, and it pays 11¢ for 3 heads, 7¢ for 2 heads, and 4e for 1 head. Is 7¢a fair price to pay to play this game? That is, does the 7¢ cost to play make the game fair? .... The 7¢ cost to play a fair price to pay because the expected winnings are (Type an integer or a fraction. Simplify your answer.)
A favorite casino game of dice “craps” is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called “craps”) the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: Provide the probability answers in fraction and in decimal forms rounded to 4 digits. A. List the possible outcomes (sample space) for winning on the first roll of the dice. B. What is the probability that a player wins the game on the first roll of the dice? C. List the possible outcomes (sample space) for losing on the first roll of the dice. D. What is the probability that a player loses the game on the…
A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers(red), as well as 0 and 00 (which are green). You bet 5 dollars that the outcome is anodd number. If you win you get 10 dollars; otherwise you lose your 5 dollars. Note:assume the 0 and 00 numbers are considered even numbers What is your expected winnings? Which of these options is best: bet on an odd number or don’t bet? Why?
A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS