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

Independent Events

Independent events are events that don't depend on each other.  If you roll a die twice in a row, the number you get on the second roll doesn't depend on the number you get on the first roll.  If you draw a pair of socks and then put them back, the second draw doesn't doesn't depend on the first draw.

We know how to figure out the probability of one event.  If we have a fair die with six sides, the odds of rolling a six is 1/6.  The probability of rolling a number less than three (1 or 2) is 2/6 = 1/3.  The probability of rolling a number greater than two (3, 4, 5, or 6) is 4/6 = 2/3.  But how do we figure out the probability of rolling two sixes in a row? Or a number less than three followed by a number greater than two? 

We can calculate the probability by brute force, but we can also reconsider counting and the general probability formula to figure out a faster and easier method.  We can also apply the method to the problem above.