Counting the number of outcomes in games of chancehas been a popular pastime for many centuries. This wasof interest not only because of the gambling that wasinvolved, but also because the outcomes of games ofchance were often interpreted as divine intent. Thus, itwas just about a thousand years ago that a bishop in whatis now Belgium determined that there are 56 different ways in which three dice can fall provided one is inter-ested only in the overall result and not in which die does what. He assigned a virtue to each of these possibilitiesand each sinner had to concentrate for some time on thevirtue that corresponded to his cast of the dice.(a) Find the number of ways in which three dice can allcome up with the same number of points.(b) Find the number of ways in which two of the threedice can come up with the same number of points, whilethe third comes up with a different number of points.(c) Find the number of ways in which all three of the dicecan come up with a different number of points.(d) Use the results of parts (a), (b), and (c) to verifythe bishop’s calculations that there are altogether 56possibilities.
Counting the number of outcomes in games of chancehas been a popular pastime for many centuries. This wasof interest not only because of the gambling that wasinvolved, but also because the outcomes of games ofchance were often interpreted as divine intent. Thus, itwas just about a thousand years ago that a bishop in whatis now Belgium determined that there are 56 different ways in which three dice can fall provided one is inter-ested only in the overall result and not in which die does what. He assigned a virtue to each of these possibilitiesand each sinner had to concentrate for some time on thevirtue that corresponded to his cast of the dice.(a) Find the number of ways in which three dice can allcome up with the same number of points.(b) Find the number of ways in which two of the threedice can come up with the same number of points, whilethe third comes up with a different number of points.(c) Find the number of ways in which all three of the dicecan come up with a different number of points.(d) Use the results of parts (a), (b), and (c) to verifythe bishop’s calculations that there are altogether 56possibilities.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.FOM: Focus On Modeling: The Monte Carlo Method
Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...
Related questions
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
Counting the number of outcomes in games of chance
has been a popular pastime for many centuries. This was
of interest not only because of the gambling that was
involved, but also because the outcomes of games of
chance were often interpreted as divine intent. Thus, it
was just about a thousand years ago that a bishop in what
is now Belgium determined that there are 56 different
has been a popular pastime for many centuries. This was
of interest not only because of the gambling that was
involved, but also because the outcomes of games of
chance were often interpreted as divine intent. Thus, it
was just about a thousand years ago that a bishop in what
is now Belgium determined that there are 56 different
ways in which three dice can fall provided one is inter-
ested only in the overall result and not in which die does
ested only in the overall result and not in which die does
what. He assigned a virtue to each of these possibilities
and each sinner had to concentrate for some time on the
virtue that corresponded to his cast of the dice.
(a) Find the number of ways in which three dice can all
come up with the same number of points.
(b) Find the number of ways in which two of the three
dice can come up with the same number of points, while
the third comes up with a different number of points.
(c) Find the number of ways in which all three of the dice
can come up with a different number of points.
(d) Use the results of parts (a), (b), and (c) to verify
the bishop’s calculations that there are altogether 56
possibilities.
and each sinner had to concentrate for some time on the
virtue that corresponded to his cast of the dice.
(a) Find the number of ways in which three dice can all
come up with the same number of points.
(b) Find the number of ways in which two of the three
dice can come up with the same number of points, while
the third comes up with a different number of points.
(c) Find the number of ways in which all three of the dice
can come up with a different number of points.
(d) Use the results of parts (a), (b), and (c) to verify
the bishop’s calculations that there are altogether 56
possibilities.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
