SI 2007: ProbabilityLing Pun & Coral Quackenbush1

SI 2007: ProbabilityLing Pun & Coral Quackenbush2 Probability: Coin Flipping and Dice Rolling By Ling Pun and Coral Quackenbush

SI 2007: ProbabilityLing Pun & Coral Quackenbush3 Objective: Sunshine Standards: MAE Collects and displays data in a variety of ways MAE Comparing experimental results with expectations Your students will be able to identify the similarities and differences of experimental versus theoretical probability and represent this data in a visual manner.

SI 2007: ProbabilityLing Pun & Coral Quackenbush4 Background and History Concepts of probability are as old as mankind itself. Pierre de Fermat Blaise Pascal Jacob Bernoulli Christiaan Huygens Pierre de Fermat, Blaise Pascal, and Christiaan Huygens gave the earliest known scientific treatment of probability.

SI 2007: ProbabilityLing Pun & Coral Quackenbush5 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 Heads: Tails:

SI 2007: ProbabilityLing Pun & Coral Quackenbush6 Representation of Probability

SI 2007: ProbabilityLing Pun & Coral Quackenbush7 Experimental versus Theoretical.. What’s the difference? Experimental probability is the result of an experiment or simulation after a large number of times. Theoretical probability is what is expected to happen based on the possible outcomes, assuming equally likely events.

SI 2007: ProbabilityLing Pun & Coral Quackenbush8 Theoretical Experimental

SI 2007: ProbabilityLing Pun & Coral Quackenbush9 Let’s simulate 10 coin flips with Excel…. It should look something like this Construct an array: Select cells C2 through C11. Select the borders & color fill.

SI 2007: ProbabilityLing Pun & Coral Quackenbush10 Use the function “=INT(2*RAND())” in each cell of the array to produce either a 1 or a 0. What function do you think we can use to simulate the experiment? Excel does not have heads and tails… what should we use? Heads = 1 Tails = 0

SI 2007: ProbabilityLing Pun & Coral Quackenbush11 Now, we need to record our data. We need to use the “sum” function. ARRAY # of HEADS (result) TOTAL TRIALS

SI 2007: ProbabilityLing Pun & Coral Quackenbush12 Select the original array and drag it to the right… Now lets try it with 100 flips….

SI 2007: ProbabilityLing Pun & Coral Quackenbush13 Now, we need to record our data. Remember: “sum” function.

SI 2007: ProbabilityLing Pun & Coral Quackenbush14 Can you adjust this situation for a six-sided number cube? Why do we multiply by “6”? Why do we add “1”? (Start New Sheet in same Excel document!)

SI 2007: ProbabilityLing Pun & Coral Quackenbush15

SI 2007: ProbabilityLing Pun & Coral Quackenbush16 One way to get a sum of 2 or 12

SI 2007: ProbabilityLing Pun & Coral Quackenbush17 Distribution of Sums Simulation of Sums