# Probability Coin Flipping and Dice Rolling

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```					SI 2007: Probability   Ling Pun & Coral Quackenbush   1
Probability:
Coin Flipping and Dice Rolling

By Ling Pun
and
Coral Quackenbush

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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.1.3.1 Collects and displays data in a variety of ways

MAE.2.3.1 Comparing experimental results with expectations

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Background and History
• Concepts of probability are as old as
mankind itself.
•Pierre de Fermat, Blaise Pascal, and
Christiaan Huygens gave the earliest
Blaise Pascal
known scientific treatment of probability.

Pierre de Fermat
Jacob Bernoulli
Christiaan Huygens

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Game of flipping a coin:
Let’s flip the coin ten times
And record how many heads or
TAILS
Tails.

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Representation of Probability

0  P( x)  1

 P( x)  1
number of favorable outcomes
Probability =
total possible outomes
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Experimental versus Theoretical..
What’s the difference?

Experimental                        Theoretical
probability is the                probability is what is
result of an                   expected to happen
experiment or                       based on the
simulation after a                 possible outcomes,
large number of                    assuming equally
times.                         likely events.

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Theoretical                           Experimental

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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

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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.

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Now, we need to record our data.

We need to use the “sum” function.
ARRAY

# of HEADS (result)                           TOTAL TRIALS
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Now lets try it with 100 flips….
Select the original array and drag it to the
right…

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Now, we need to record our data.

Remember: “sum” function.

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for a six-sided number cube?
(Start New Sheet in same Excel document!)

Why do we multiply by “6”?

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One way to get a
sum of 2 or 12

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Distribution of Sums

Simulation of Sums

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