In the game of craps, a player rolls two regular dice. She wins at once if the total is 7 or 11, and loses at once if the total is 2, 3, or 12. Otherwise, she continues rolling the two dice until she either wins by seeing her initial total again before seeing 7, or loses by seeing 7. Let A be the event "She wins the game" and let B; be the event "The total from rolling two dice is i", i = 2, 3, ..., 12. a. Let p = P(B5) and q = P(B7). Suppose that the player's initial total is 5, show in detail that the probability she wins is p/(p + q). b. Find P(A | B6) and P(A | B3). c. Show that the probability she wins the game of craps is 0.493. d. If she plays craps 99 times, what is the probability she wins more than half the time? You may use R to calculate binomial probabilities.

In the game of craps, a player rolls two regular dice. She wins at once if the total is 7 or 11, and loses at once if the total is 2, 3, or 12. Otherwise, she continues rolling the two dice until she either wins by seeing her initial total again before seeing 7, or loses by seeing 7. Let A be the event "She wins the game" and let B; be the event "The total from rolling two dice is i", i = 2, 3, ..., 12. a. Let p = P(B5) and q = P(B7). Suppose that the player's initial total is 5, show in detail that the probability she wins is p/(p + q). b. Find P(A | B6) and P(A | B3). c. Show that the probability she wins the game of craps is 0.493. d. If she plays craps 99 times, what is the probability she wins more than half the time? You may use R to calculate binomial probabilities.

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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