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Probability
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= "She wins the game" and B = "The total from rolling two dice is i", i = 2,3,...,12. (a) Find P(A | B7) and P(A | B₂). (b) Let p= P(B5) and q = P(B7). Suppose that the player's initial total is 5. Show in detail the probability she wins is p/(p+q). (e) Show that the probability she wins the game of craps is 0.493.

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= "She wins the game" and B = "The total from rolling two dice is i", i = 2,3,...,12. (a) Find P(A | B7) and P(A | B₂). (b) Let p= P(B5) and q = P(B7). Suppose that the player's initial total is 5. Show in detail the probability she wins is p/(p+q). (e) Show that the probability she wins the game of craps is 0.493.

A First Course in Probability (10th Edition)
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 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 = "She wins the game" and B;= "The total from rolling two dice is i", i = 2,3,...,12. (a) Find P(A | B7) and P(A | B₂). (b) Let p = P(B5) and q = P(B7). Suppose that the player's initial total is 5. Show in detail the probability she wins is p/(p+q). (c) Show that the probability she wins the game of craps is 0.493.
Transcribed Image Text: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 = "She wins the game" and B;= "The total from rolling two dice is i", i = 2,3,...,12. (a) Find P(A | B7) and P(A | B₂). (b) Let p = P(B5) and q = P(B7). Suppose that the player's initial total is 5. Show in detail the probability she wins is p/(p+q). (c) Show that the probability she wins the game of craps is 0.493.
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