Solution Found!
If the die in assumed fair, calculate the probabilities
Chapter 4, Problem 8P(choose chapter or problem)
Problem 8P
If the die in Problem is assumed fair, calculate the probabilities associated with the random variables in parts (a) through (d).
Problem
Suppose that a die is rolled twice. What are the possible values that the following random variables can take on:
(a) the maximum value to appear in the two rolls;
(b) the minimum value to appear in the two rolls;
(c) the sum of the two rolls;
(d) the value of the first roll minus the value of the second roll?
Questions & Answers
QUESTION:
Problem 8P
If the die in Problem is assumed fair, calculate the probabilities associated with the random variables in parts (a) through (d).
Problem
Suppose that a die is rolled twice. What are the possible values that the following random variables can take on:
(a) the maximum value to appear in the two rolls;
(b) the minimum value to appear in the two rolls;
(c) the sum of the two rolls;
(d) the value of the first roll minus the value of the second roll?
ANSWER:
Solution
Step 1 of 5
Given that 2 dice are rolled twice
The following table represents the maximum, minimum, sum and first minus second die observed when we rolled two dice
Die 1 |
1 |
2 |
3 |
4 |
5 |
6 |
1 |
(1,1,2,0) |
(2,1,3,-1) |
(3,1,4,-2) |
(4,1,5,-3) |
(5,1,6,-4) |
(6,1,7,-5) |
2 |
(2,1,3,1) |
(2,2,4,0) |
(3,2,5,-1) |
(4,2,6,-2) |
(5,2,7,-3) |
(6,2,8,-4) |
3 |
(3,1,4,2) |
(3,2,5,1) |
(3,3,6,0) |
(4,3,7,-1) |
(5,3,8,-2) |
(6,3,9,-3) |
4 |
(4,1,5,3) |
(4,2,6,2) |
(4,3,7,1) |
(4,4,8,0) |
(5,4,9,-1) |
(6,4,10,-2) |
5 |
(5,1,6,4) |
(5,2,7,3) |
(5,3,8,2) |
(5,4,9,1) |
(5,5,10,0) |
(6,5,11,-1) |
6 |
(6,1,7,5) |
(6,2 ,8,4) |
(6,3,9,3) |
(6,4,10,2) |
(6,5,11,1) |
(6,6,12,0) |