# Probability Dice Game

### What You Need:

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

### What You Do:

1. Tell your child that he's going to learn all about probability using nothing but 2 dice.
2. Ask him how many different outcomes are possible if he was 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 + 66 + 12 + 55 + 23 + 44 + 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 figure out 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

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

Take It Further:

Here’s a dice challenge for you: First, tell your kid the roll you want him to try and get. Then, give him two chances to roll. If he rolls what you requested, he receives a reward (a small piece of candy). He can win another for Correctly Guessing the probability of rolling whatever you asked him to roll. 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” OrAn “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” OrA “6” OrA “7” OrAn “11” (1/36 + 5/36 + 6/36 + 2/36 = 14/36 = 7/18)

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