Probability Dice Game

What You Do:

1. Tell your child that you’re going to learn all about dice and probability.
2. Ask him how many different ways there are to roll 2 dice. Remind him that there are 6 options on both sides. Together, you can determine that there are 6 x 6 = 36 possible rolls.
3. Ask him how many ways there are to roll a total of “2” using two dice. After thinking, he should conclude that there’s only one way: 1 + 1
4. Ask him how many ways there are to roll a total of “7.” He should come up with 6 combinations: 1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3.
5. Time to figure out all of the rolls. Have him fill out the last two columns of the following chart. He has already figured out “2” and “7,” and he can do the rest the same way.

Total to Roll	Ways to Get the Total	Probability of that Roll
2	1	1 /36
3		/ 36
4		/ 36
5		/ 36
6		/ 36
7	6	6 /36 = 1/6
8		/ 36
9		/ 36
10		/ 36
11		/ 36
12		/ 36

  
 
6. When he’s done, the chart should look like this:
 

Total to Roll	Ways to Get the Total	Probability of that Roll
2	1	1 / 36
3	2	2 / 36 = 1/18
4	3	3 / 36 = 1/12
5	4	4 / 36 = 1/9
6	5	5 / 36
7	6	6 / 36 = 1/6
8	5	5 / 36
9	4	4 / 36 = 1/9
10	3	3 / 36 = 1/12
11	2	2  / 36 = 1/18
12	1	1 / 36

 
7. Here’s a dice challenge for him. First, tell him the roll you want him to try and get. Then, give him two opportunities to win a reward (like a small piece of candy.) He can win an award if he rolls what you asked him to get. And, he can win another award for guessing the correct probability of rolling what you’ve asked of him. Good luck!
   • Roll a total of “9”                     (1/9)
   • Roll a total of “11”                    (1/18)
   • Roll a total of 8”                       (5/36)  
   • Roll a total of “12”                    (1/36)
   • Roll a total of “5”                      (1/9)
   • Roll a “7” or an “11”  (6/36 + 2/36 = 8/36 = 2/9)
   • Roll a “2” or “6”                      (1/36 + 5/36 = 6/36 = 1/6 )
   • Roll a “2” or a “6” or a “7” or an “11” (1/36 + 5/36 + 6/36 + 2/36 = 14/36 = 7/18)
   • You can make up your own as you go