Probability: Coin Flipping and Dice Rolling

1. Ling Pun & Coral Quackenbush

2. Probability:Coin Flipping and Dice Rolling By Ling Pun and Coral Quackenbush Ling Pun & Coral Quackenbush

3. Objective: Your students will be able to identify the similarities and differences of experimental versus theoretical probability and represent this data in a visual manner. Sunshine Standards: MAE.1.3.1Collects and displays data in a variety of ways MAE.2.3.1 Comparing experimental results with expectations Ling Pun & Coral Quackenbush

4. Jacob Bernoulli Pierre de Fermat Blaise Pascal Christiaan Huygens Background and History • Concepts of probability are as old as • mankind itself. • Pierre de Fermat, Blaise Pascal, and Christiaan Huygens gave the earliest known scientific treatment of probability. Ling Pun & Coral Quackenbush

5. HEADS TAILS Game of flipping a coin: Let’s flip the coin ten times And record how many heads or Tails. What are your results ? Heads: Tails: Ling Pun & Coral Quackenbush

6. Representation of Probability Ling Pun & Coral Quackenbush

7. Theoretical probability is what is expected to happen based on the possible outcomes, assuming equally likely events. Experimental versus Theoretical.. What’s the difference? Experimental probability isthe result of an experiment or simulation after a large number of times. Ling Pun & Coral Quackenbush

8. Experimental Theoretical Ling Pun & Coral Quackenbush

9. Let’s simulate 10 coin flips with Excel…. • Construct an array: • Select cells C2 through C11. • Select the borders & color fill. It should look something like this Ling Pun & Coral Quackenbush

10. Excel does not have heads and tails… what should we use? Heads = 1 Tails = 0 What function do you think we can use to simulate the experiment? Use the function “=INT(2*RAND())” in each cell of the array to produce either a 1 or a 0. Ling Pun & Coral Quackenbush

11. Now, we need to record our data. We need to use the “sum” function. ARRAY # of HEADS (result) TOTAL TRIALS Ling Pun & Coral Quackenbush

12. Now lets try it with 100 flips…. Select the original array and drag it to the right… Ling Pun & Coral Quackenbush

13. Now, we need to record our data. Remember: “sum” function. Ling Pun & Coral Quackenbush

14. Why do we multiply by “6”? Why do we add “1”? Can you adjust this situation for a six-sided number cube? (Start New Sheet in same Excel document!) Ling Pun & Coral Quackenbush

15. Ling Pun & Coral Quackenbush

16. One way to get a sum of 2 or 12 Ling Pun & Coral Quackenbush

17. Distribution of Sums Simulation of Sums Ling Pun & Coral Quackenbush