Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
B. Suppose a die is tossed 3 times. We can represent an outcome of this process by an ordered 3- tuple where the ith coordinate represents the number of dots on the ih toss. Let 2-set of all possible outcomes={(X1, X2, X3) X₁E {1,2,3,4,5,6), i=1,2,3). Define Aij = the set containing outcomes where i dots appear on the jth toss, i=1,2,3,4,5,6 and j=1,2,3. For example, A1,2 = the set containing outcomes where 1 dot appears on the 2nd toss = {(1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6), (2,1,1), (2,1,2), (2,1,3), (2,1,4), (2,1,5), (2,1,6), (3,1,1), (3,1,2), (3,1,3), (3,1,4), (3,1,5), (3,1,6), (4,1,1), (4,1,2), (4,1,3), (4,1,4), (4,1,5), (4,1,6), (5,1,1), (5,1,2), (5,1,3), (5,1,4), (5,1,5), (5,1,6), (6,1,1), (6,1,2), (6,1,3), (6,1,4), (6,1,5), (6,1,6)} 1. Specify the set A-A3,2 A5,3 using the roster method. Note: You cannot use the ellipsis in your specification.

B. Suppose a die is tossed 3 times. We can represent an outcome of this process by an ordered 3- tuple where the ith coordinate represents the number of dots on the ih toss. Let 2-set of all possible outcomes={(X1, X2, X3) X₁E {1,2,3,4,5,6), i=1,2,3). Define Aij = the set containing outcomes where i dots appear on the jth toss, i=1,2,3,4,5,6 and j=1,2,3. For example, A1,2 = the set containing outcomes where 1 dot appears on the 2nd toss = {(1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6), (2,1,1), (2,1,2), (2,1,3), (2,1,4), (2,1,5), (2,1,6), (3,1,1), (3,1,2), (3,1,3), (3,1,4), (3,1,5), (3,1,6), (4,1,1), (4,1,2), (4,1,3), (4,1,4), (4,1,5), (4,1,6), (5,1,1), (5,1,2), (5,1,3), (5,1,4), (5,1,5), (5,1,6), (6,1,1), (6,1,2), (6,1,3), (6,1,4), (6,1,5), (6,1,6)} 1. Specify the set A-A3,2 A5,3 using the roster method. Note: You cannot use the ellipsis in your specification.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 29E
See similar textbooks
icon
Related questions
Question
B. 1 Only
B. Suppose a die is tossed 3 times. We can represent an outcome of this process by an ordered 3- tuple where the ith coordinate represents the number of dots on the ih toss. Let 2-set of all possible outcomes={(X1, X2, X3) XiE {1,2,3,4,5,6), i=1,2,3). Define Aij = the set containing outcomes where i dots appear on the jth toss, i=1,2,3,4,5,6 and j=1,2,3. For example, A1,2 = the set containing outcomes where 1 dot appears on the 2nd toss = {(1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6), (2,1,1), (2,1,2), (2,1,3), (2,1,4), (2,1,5), (2,1,6), (3,1,1), (3,1,2), (3,1,3), (3,1,4), (3,1,5), (3,1,6), (4,1,1), (4,1,2), (4,1,3), (4,1,4), (4,1,5), (4,1,6), (5,1,1), (5,1,2), (5,1,3), (5,1,4), (5,1,5), (5,1,6), (6,1,1), (6,1,2), (6,1,3), (6,1,4), (6,1,5), (6,1,6)} 1. Specify the set A=A3,2 A5,3 using the roster method. Note: You cannot use the ellipsis in your specification. 2. Let B=set containing outcomes where 2 dots appear in all 3 tosses. Express set B as a composition of the Aij. 3. Let C = set containing outcomes where 4 dots appear in exactly 2 tosses. Express C as a composition of the Aij.
Transcribed Image Text:B. Suppose a die is tossed 3 times. We can represent an outcome of this process by an ordered 3- tuple where the ith coordinate represents the number of dots on the ih toss. Let 2-set of all possible outcomes={(X1, X2, X3) XiE {1,2,3,4,5,6), i=1,2,3). Define Aij = the set containing outcomes where i dots appear on the jth toss, i=1,2,3,4,5,6 and j=1,2,3. For example, A1,2 = the set containing outcomes where 1 dot appears on the 2nd toss = {(1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6), (2,1,1), (2,1,2), (2,1,3), (2,1,4), (2,1,5), (2,1,6), (3,1,1), (3,1,2), (3,1,3), (3,1,4), (3,1,5), (3,1,6), (4,1,1), (4,1,2), (4,1,3), (4,1,4), (4,1,5), (4,1,6), (5,1,1), (5,1,2), (5,1,3), (5,1,4), (5,1,5), (5,1,6), (6,1,1), (6,1,2), (6,1,3), (6,1,4), (6,1,5), (6,1,6)} 1. Specify the set A=A3,2 A5,3 using the roster method. Note: You cannot use the ellipsis in your specification. 2. Let B=set containing outcomes where 2 dots appear in all 3 tosses. Express set B as a composition of the Aij. 3. Let C = set containing outcomes where 4 dots appear in exactly 2 tosses. Express C as a composition of the Aij.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS