# SAT Snake Eyes

### What You Need:

• A pair of dice, two different colors (I’ll use red and blue for examples)
• A piece of paper
• Some M&M’s or another little treat

### What You Do:

 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

 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

Extension:

Tell your teen, if he doesn't already know, that the game “Craps” is all about rolling two dice over and over. Ask himif he could figure out why “7,” “2,” and “12” are the most important rolls. If you know more about the game, it’s a great way to teach probability.

1. Tell your teen 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 ways: 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.
6. When he’s done, the chart should look like this:
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