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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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