Documents

  1. Single 9-block
  2. Thirty-two 9-blocks
  3. Template for 3zees
  4. Sample Distribution
  5. Guide to Sample Stalagmite Model

Netlogo Models

  1. 9 Blocks
  2. Sample Stalagmite
  3. Sampler
  4. Sampler client

Discussions

  1. Ways of Counting
  2. Tree Counting
  3. Binary Counting
  4. Concatenation
  5. Two Square Concatenation
  6. Other Concatenations
  7. Quantity Groups
  8. Independent Events
  9. Dependent Events
  10. Calculating Probability
  11. Counting Reconsidered
  12. Probabiliy Formula
  13. Independent Events Formula
  14. Apply Independent Events Formula
  15. Stalagmite Riddle

Related Links

Calculating Probability

Let's calculate the probability of rolling two sixes.  We can start by looking at all the pairs that can possibly be rolled:

1-1

1-2

1-3

1-4

1-5

1-6

2-1

2-2

2-3

2-4

2-5

2-6

3-1

3-2

3-3

3-4

3-5

3-6

4-1

4-2

4-3

4-4

4-5

4-6

5-1

5-2

5-3

5-4

5-5

5-6

6-1

6-2

6-3

6-4

6-5

6-6

There are thirty-six possibilities all together (notice that 36=6*6=6^2).  Out of those, there is only one pair that is 6-6, so the odds of rolling 6-6 is 1/36.

Now consider the probability of rolling a number less than three followed by a number greater than two.  How many ways can we do this?  For the first number, we can roll a one or a two.  For each of these two choices, we can roll either a 3, 4, 5, or 6:

1-3

1-4

1-5

1-6

2-3

2-4

2-5

2-6

So there are eight ways that we can get the desired events (two ways to get a number less than three followed by four ways to get a number greater than two--2*4=8).  Since we have already shown that there are 36 possible combinations, the probability of our two independent events is 8/36 = 2/9.