Composing with Random Numbers

         I happened across this game in my files. I used it with my middle school students as part of a unit about the science of sound and music. I think it would also make a great challenge for teens learning to code. This activity is based on a musical game that Mozart and his friends supposedly played.

(If you’re already familiar with how to calculate probabilities with dice, feel free to skip to Part II)

First, let’s calculate the probability of various rolls of a pair of dice: Let’s make a chart of all the possible outcomes of rolling two dice.  Each die has 6 sides, so we’ll use a 6 X 6 matrix

Die roll	1	2	3	4	5	6
1	2	3	4	5	6	7
2	3	4	5	6	7	8
3	4	5	6	7	8	9
4	5	6	7	8	9	10
5	6	7	8	9	10	11
6	7	8	9	10	11	12

The probability of an event is calculated by counting the number of possible ways of getting a particular outcome (such as rolling a 9 on the dice), and dividing by the total number of possibilities.  Probability is expressed as either a fraction or a decimal.  The probability of an event is always somewhere between 0 (impossible) and 1 (certain).

How many possible outcomes are there when you roll two dice?  _______

How many different ways can you roll a 9?  __________

So the probability of rolling a 9 is : __________  (express as a fraction)

Refer to the matrix above.  What is the probability of each possible roll of two dice.

2: __________                                                            8: __________ 

3: __________                                                            9: __________ 

4: __________                                                            10: __________ 

5: __________                                                            11: __________ 

6: __________                                                            12: __________ 

7: __________ 

[Check Your Answers Here]

Now lets create a composition: Go to Part II