Probability: Coin Flipping and Dice Rolling

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

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### Probability:Coin Flipping and Dice Rolling

By Ling Pun

and

Coral Quackenbush

Ling Pun & Coral Quackenbush

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

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

TAILS

Game of flipping a coin:

Let’s flip the coin ten times

And record how many heads or

Tails.

Tails:

Ling Pun & Coral Quackenbush

Representation of Probability

Ling Pun & Coral Quackenbush

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

Experimental

Theoretical

Ling Pun & Coral Quackenbush

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

Excel does not have heads and tails… what should we use?

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

Now, we need to record our data.

We need to use the “sum” function.

ARRAY

TOTAL TRIALS

Ling Pun & Coral Quackenbush

Now lets try it with 100 flips….

Select the original array and drag it to the right…

Ling Pun & Coral Quackenbush

Now, we need to record our data.

Remember: “sum” function.

Ling Pun & Coral Quackenbush

Why do we multiply by “6”?

Can you adjust this situation for a six-sided number cube?

(Start New Sheet in same Excel document!)

Ling Pun & Coral Quackenbush

One way to get a sum of 2 or 12

Ling Pun & Coral Quackenbush

Distribution of Sums

Simulation of Sums

Ling Pun & Coral Quackenbush