(12.06) Computer games in which the players take the roles of characters are ver

Question

(12.06) Computer games in which the players take the roles of characters are very popular. They go back to earlier tabletop games such as Dungeons & Dragons. These games use many different types of dice. A four-sided die has faces with 1, 2, 3, and 4 spots.

Step 1:
What is the sample space for rolling the die twice (spots on first and second rolls)? Follow the example of Figure 12.2, below.

S = {1,2,3,4,5,6,7,8} S = {1,2,3,4} S = {2,4,6,8} S = {2,3,4,5,6,7,8}

What is the assignment of probabilities to outcomes in this sample space?
Assume that the die is perfectly balanced, and follow the method of Example 11.4.

Step 2:
In this probability model, what is the probability of 2 spots? 6/16 4/16 1/16 11/16 14/16 7/16 0 15/16 2/16 10/16 3/16 9/16 8/16 12/16 1 5/16 13/16


Step 3:
In this probability model, what is the probability of 4 spots? 6/16 15/16 4/16 1 2/16 1/16 3/16 8/16 9/16 5/16 12/16 11/16 10/16 13/16 14/16 7/16 0


Step 4:
In this probability model, what is the probability of 5 spots? 3/16 1/16 7/16 8/16 13/16 6/16 2/16 0 14/16 1 11/16 10/16 4/16 15/16 5/16 9/16 12/16


Step 5:
In this probability model, what is the probability of 1 spot? 13/16 3/16 1 4/16 0 10/16 14/16 9/16 6/16 7/16 2/16 11/16 5/16 1/16 15/16 8/16 12/16

Explanation / Answer

1) S = {2,3,4,5,6,7,8}

2) probability of 2 spots =P(1 spot on 1st and 1 spot on 2nbd) =(!/4)*(!/4) =1/16

3) probability of 4 spots =P(1 spot on 1st and 3 on 2nd+2 spot on first and 2 on 2nd+3 on first and 1 on second)

=3/16

4)probability of 5 spots =P(1 spot on 1st and 4 on 2nd+2 spot on 1st and 3 on 2nd+3 spot on 1st and 2 on 2nd+4 spot on first and 1 on 2nd)=4/16 =4/16

5)probability of 1 spot =0

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