Part 1: Let’s play “Craps” 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. List the possible outcomes (sample space) for winning on the first roll of the dice. What is the probability that a player wins the game on the first roll of the dice? List the possible outcomes (sample space) for losing on the first roll of the dice. What is the probability that a player loses the game on the first roll of the dice? If the player throws a total of 4 on the first roll, what is the probability that the player wins in the next roll? If the player throws a total of 6 on the first roll, what is the probability that the player loses in the next roll?

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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Part 1: Let’s play “Craps”

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.

List the possible outcomes (sample space) for winning on the first roll of the dice.

What is the probability that a player wins the game on the first roll of the dice?

List the possible outcomes (sample space) for losing on the first roll of the dice.

What is the probability that a player loses the game on the first roll of the dice?

If the player throws a total of 4 on the first roll, what is the probability that the player wins in the next roll?

If the player throws a total of 6 on the first roll, what is the probability that the player loses in the next roll?

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