1. I have two 6-sided dice. One is numbered 1-6, and the other is numbered 5-10.
What is the probability that when I roll them I will get...
| + | 1 | 2 | 3 | 4 | 5 | 6 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 |
What is the most likely sum? 11
2. Josh, Sarah, Kelly and Brian had these dice
Josh: 2, 2, 2, 2, 6, 6
Sarah:3, 3, 3, 3, 3, 3
Kelly: 4, 4, 4, 4, 0, 0
Brian: 1, 1, 1, 5, 5, 5
a. If Josh and Sarah both roll their dice, who will have the higher number more often? What is the probability Josh will have the higher number?
| larger J or S? | 2 | 2 | 2 | 2 | 6 | 6 |
| 3 | S | S | S | S | J | J |
| 3 | S | S | S | S | J | J |
| 3 | S | S | S | S | J | J |
| 3 | S | S | S | S | J | J |
| 3 | S | S | S | S | J | J |
| 3 | S | S | S | S | J | J |
Sarah's die will be higher more often. The probability that Josh's die is higher is 12/36=1/3
b. If Josh and Sarah both roll their dice, and they add the numbers, what is the probability that the sum will be:
| + | 2 | 2 | 2 | 2 | 6 | 6 |
| 3 | 5 | 5 | 5 | 5 | 9 | 9 |
| 3 | 5 | 5 | 5 | 5 | 9 | 9 |
| 3 | 5 | 5 | 5 | 5 | 9 | 9 |
| 3 | 5 | 5 | 5 | 5 | 9 | 9 |
| 3 | 5 | 5 | 5 | 5 | 9 | 9 |
| 3 | 5 | 5 | 5 | 5 | 9 | 9 |
c. If Sarah and Kelly both roll their dice, who will have the higher number more often? What is the probability that Sarah will have the higher number?
Sarah:3, 3, 3, 3, 3, 3
Kelly: 4, 4, 4, 4, 0, 0
| larger S or K? | 4 | 4 | 4 | 4 | 0 | 0 |
| 3 | K | K | K | K | S | S |
| 3 | K | K | K | K | S | S |
| 3 | K | K | K | K | S | S |
| 3 | K | K | K | K | S | S |
| 3 | K | K | K | K | S | S |
| 3 | K | K | K | K | S | S |
Kelly's die will be higher more often. The probability that Sarah's die is higher is 12/36=1/3
d. If Kelly and Brian both roll their dice, who will have the higher number more often? What ist he probability that Brian will have the higher number?
Kelly: 4, 4, 4, 4, 0, 0
Brian: 1, 1, 1, 5, 5, 5
| larger K or B? | 4 | 4 | 4 | 4 | 0 | 0 |
| 1 | K | K | K | K | B | B |
| 1 | K | K | K | K | B | B |
| 1 | K | K | K | K | B | B |
| 5 | B | B | B | B | B | B |
| 5 | B | B | B | B | B | B |
| 5 | B | B | B | B | B | B |
Brian's die will be larger more often. The probability that Brian's die is higher is 24/36=2/3
e. If Kelly and Brian both roll their dice, and they add the numbers, what is the probability that the sum will be:
| + | 4 | 4 | 4 | 4 | 0 | 0 |
| 1 | 5 | 5 | 5 | 5 | 1 | 1 |
| 1 | 5 | 5 | 5 | 5 | 1 | 1 |
| 1 | 5 | 5 | 5 | 5 | 1 | 1 |
| 5 | 9 | 9 | 9 | 9 | 5 | 5 |
| 5 | 9 | 9 | 9 | 9 | 5 | 5 |
| 5 | 9 | 9 | 9 | 9 | 5 | 5 |
f. If Brian and Josh both roll their dice, who will have the higher number more often? What is the probability Brian will have the higher number?
Josh: 2, 2, 2, 2, 6, 6
Brian: 1, 1, 1, 5, 5, 5
| larger J or B? | 2 | 2 | 2 | 2 | 6 | 6 |
| 1 | J | J | J | J | J | J |
| 1 | J | J | J | J | J | J |
| 1 | J | J | J | J | J | J |
| 5 | B | B | B | B | J | J |
| 5 | B | B | B | B | J | J |
| 5 | B | B | B | B | J | J |
Josh will have the higher number more often.
The probability that Brian's number is higher is 12/36=1/3
g. Put the dice in order so that person 1 beats person2, person 2 beats person 3, person3 beats person 4 but person 4 beats person 1 (see page 539#6)
Josh is higher more often compared to Brian; Brian's die is higher more often to Kelly. Kelly's die is higher more often compared to Sarah. Sarah's die is higher more often compared to Josh