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In the gambling game “craps,” a pair of dice is rolled and

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 13E Chapter 1.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 13E

PROBLEM 13E

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 l0, 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).

(c) Given that 8 is the outcome on the first roll, find the probability that the bettor now rolls the point 8 before rolling a 7 and thus wins. Note that at this stage in the game the only outcomes of interest are 7 and 8. Thus find P(8 |7 or 8).

(d) The probability that a bettor rolls an 8 on the first roll and then wins is given by P(8)P(8 | 7 or 8). Show that this probability is (5/36)(5/11).

(e) Show that the total probability that a bettor wins in the game of craps is 0.49293. Hint: Note that the bettor can win in one of several mutually exclusive ways: by rolling a 7 or an 11 on the first roll or by establishing one of the points 4, 5, 6, 8, 9, or 10 on the first roll and then obtaining that point on successive rolls before a 7 comes up.

Step-by-Step Solution:

Answer

Step 1 of 6

a)When you roll 2 dice the no.of outcomes=36

The 36 outcomes are

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)


Step 2 of 6

Chapter 1.3, Problem 13E is Solved
Step 3 of 6

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. Since the solution to 13E from 1.3 chapter was answered, more than 683 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 13E from chapter: 1.3 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. The answer to “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 l0, 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).(c) Given that 8 is the outcome on the first roll, find the probability that the bettor now rolls the point 8 before rolling a 7 and thus wins. Note that at this stage in the game the only outcomes of interest are 7 and 8. Thus find P(8 |7 or 8).(d) The probability that a bettor rolls an 8 on the first roll and then wins is given by P(8)P(8 | 7 or 8). Show that this probability is (5/36)(5/11).(e) Show that the total probability that a bettor wins in the game of craps is 0.49293. Hint: Note that the bettor can win in one of several mutually exclusive ways: by rolling a 7 or an 11 on the first roll or by establishing one of the points 4, 5, 6, 8, 9, or 10 on the first roll and then obtaining that point on successive rolls before a 7 comes up.” is broken down into a number of easy to follow steps, and 315 words. This full solution covers the following key subjects: bettor, Roll, Probability, point, wins. This expansive textbook survival guide covers 59 chapters, and 1476 solutions.

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