humber of spots showing is five. Follow that method to give a probability model for the total number of spots. The possible outcomes are 2, 3, 4, ..., 12. Then use the probabilities to find the expected value of the total.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
20.16 Rolling two dice. Example 2 of Chapter 18 (page 428) gives a probability model for
rolling two casino dice and recording the number of spots on each of the two up-faces. That
example also shows how to find the probability that the total number of spots showing is
five. Follow that method to give a probability model for the total number of spots. The
possible outcomes are 2, 3, 4, ... , 12. Then use the probabilities to find the expected value of
the total.
Transcribed Image Text:20.16 Rolling two dice. Example 2 of Chapter 18 (page 428) gives a probability model for rolling two casino dice and recording the number of spots on each of the two up-faces. That example also shows how to find the probability that the total number of spots showing is five. Follow that method to give a probability model for the total number of spots. The possible outcomes are 2, 3, 4, ... , 12. Then use the probabilities to find the expected value of the total.
Arthur-studio10/Shutterstock
Rolling two dice is a common way to lose money in casinos. There are 36 possible outcomes
when we roll two dice and record the up-faces in order (first die, second die). Figure 18.1
displays these outcomes. What probabilities should we assign?
国国图国
国口 国回 围图 国图 围
Moore/Notz, Statistics: Concepts and Controversies, 10e, © 2020 W. H. Freeman and Company
Figure 18.1 The 36 possible outcomes from rolling two dice, Example 2.
The outcomes are as follows: (1, 1); (2, 1); (3, 1); (4, 1); (5, 1); (6, 1); (1, 2); (1, 2); (3, 2); (4,
2); (5, 2); (6, 2); (1, 3); (2, 3); (3, 3); (4, 3); (5, 3); (6, 3); (1, 4); (2, 4); (3, 4); (4, 4); (5, 4); (6,
4); (1, 5); (2, 5); (3, 5); (6, 5); (1, 6); (2, 6); (3, 6); (4, 6); (5, 6); and (6, 6).
Casino dice are carefully made. Their spots are not hollowed out, which would give the faces
different weights, but are filled with white plastic of the same density as the red plastic of the
body. For casino dice, it is reasonable to assign the same probability to each of the 36
outcomes in Figure 18.1. Because these 36 probabilities must have sum 1 (Rule B), each
outcome must have probability 1/36, or 1-in-36.
We are interested in the sum of the spots on the up-faces of the dice. What is the probability
that this sum is 5? The event "roll a 5" contains four outcomes, and its probability is the sum
of the probabilities of these outcomes:
P(roll a 5)
+P
+P
+P
1
1
1
36
36
36
36
4
= 0.111
36
:: ::
• 1. 1.:1::::
Transcribed Image Text:Arthur-studio10/Shutterstock Rolling two dice is a common way to lose money in casinos. There are 36 possible outcomes when we roll two dice and record the up-faces in order (first die, second die). Figure 18.1 displays these outcomes. What probabilities should we assign? 国国图国 国口 国回 围图 国图 围 Moore/Notz, Statistics: Concepts and Controversies, 10e, © 2020 W. H. Freeman and Company Figure 18.1 The 36 possible outcomes from rolling two dice, Example 2. The outcomes are as follows: (1, 1); (2, 1); (3, 1); (4, 1); (5, 1); (6, 1); (1, 2); (1, 2); (3, 2); (4, 2); (5, 2); (6, 2); (1, 3); (2, 3); (3, 3); (4, 3); (5, 3); (6, 3); (1, 4); (2, 4); (3, 4); (4, 4); (5, 4); (6, 4); (1, 5); (2, 5); (3, 5); (6, 5); (1, 6); (2, 6); (3, 6); (4, 6); (5, 6); and (6, 6). Casino dice are carefully made. Their spots are not hollowed out, which would give the faces different weights, but are filled with white plastic of the same density as the red plastic of the body. For casino dice, it is reasonable to assign the same probability to each of the 36 outcomes in Figure 18.1. Because these 36 probabilities must have sum 1 (Rule B), each outcome must have probability 1/36, or 1-in-36. We are interested in the sum of the spots on the up-faces of the dice. What is the probability that this sum is 5? The event "roll a 5" contains four outcomes, and its probability is the sum of the probabilities of these outcomes: P(roll a 5) +P +P +P 1 1 1 36 36 36 36 4 = 0.111 36 :: :: • 1. 1.:1::::
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman