Transcript Probability: Coin Flipping and Dice Rolling

SI 2007: Probability
Ling Pun & Coral Quackenbush
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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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Ling Pun & Coral Quackenbush
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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
known scientific treatment of probability.
Jacob Bernoulli
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Blaise Pascal
Pierre de Fermat
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.
HEADS
TAILS
What are your results ?
Heads:
SI 2007: Probability
Ling Pun & Coral Quackenbush
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
probability is the
result of an
experiment or
simulation after a
large number of
times.
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Theoretical
probability is what is
expected to happen
based on the
possible outcomes,
assuming equally
likely events.
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Theoretical
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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)
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Ling Pun & Coral Quackenbush
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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Can you adjust this situation
for a six-sided number cube?
(Start New Sheet in same Excel document!)
Why do we multiply by “6”?
Why do we add “1”?
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Ling Pun & Coral Quackenbush
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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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