This document discusses developing probability models to predict the outcomes of chance processes like spinning a penny or tossing a paper cup. It introduces the concepts of sample space, predicted probabilities, and experimental probabilities. Students are asked to predict probabilities for penny spins and cup tosses, then test their predictions experimentally. The results show that a penny's probabilities are close to equal, while a cup's probabilities differ, likely due to its shape. Modifying a cup's shape could change the probabilities. The document also notes that spun coins may land with unequal probabilities due to weight imbalance.

1. Day 15 Probability Models.notebook April 03, 2013
AIM: Probability Models
Do Now
The star basketball player for a professional basketball team
gets hurt of the way through the last basketball season. On
the timeline below are the wins and losses of the team with and
without their star player.
29 wins and 11 losses 7 wins and 13 losses
Start of season End of Season
Injury!
This year the team expects to play the same number of games
as last year, and their star player will only miss the first quarter
of the year. If the team maintains the same proportion of wins
and losses with and without their star player as they did last
year, approximately how many games should fans expect the
team win this year?
A 24
B 27
C 36
D 38
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2. Day 15 Probability Models.notebook April 03, 2013
Common Core Math Standard 7.SP.7
Develop a probability model (which may not be uniform) by observing
frequencies in data generated from a chance process.
For example, find the approximate probability that a spinning penny
will land heads up or that a tossed paper cup will land open-end down.
Do the outcomes for the spinning penny appear to be equally likely
based on the observed frequencies?
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3. Day 15 Probability Models.notebook April 03, 2013
Anticipatory Set
Today we will create a Probability Model for spinning a
penny and tossing a paper cup. A Probability Model is a
mathematical representation of a random phenomenon,
which includes the sample space and the probability
associated with each event.
Sample Space of Spinning a Penny:
Sample Space of Tossing a Paper Cup:
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4. Day 15 Probability Models.notebook April 03, 2013
Predicted Probabilities associated with Spinning a Penny:
Predicted Probabilities associated with Tossing a Paper Cup:
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5. Day 15 Probability Models.notebook April 03, 2013
Questions:
1.) Explain your predicted probabilities associated
with Spinning a Penny.
2.) Explain your predicted probabilities associated
with Tossing a Paper Cup.
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6. Day 15 Probability Models.notebook April 03, 2013
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7. Day 15 Probability Models.notebook April 03, 2013
Experimental Probabilities associated with Spinning a Penny:
Experimental Probabilities associated with Tossing a Paper
Cup:
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8. Day 15 Probability Models.notebook April 03, 2013
Questions:
1.) How did your predicted probabilities compare with the
experimental probabilities?
2.) What are the key differences between a penny and a cup that
effects the probability models?
3.) How would you re-design the cup to increase the likelihood of
the cup landing open-end down.
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9. Day 15 Probability Models.notebook April 03, 2013
Coin Spin Unfair?
If the coin is spun, rather than tossed, it can have a much­larger­than­50% chance of ending with the
heavier side down. Spun coins can exhibit “huge bias” (some spun coins will fall tails­up 80% of the
time).
Coin Flipper
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10. Day 15 Probability Models.notebook April 03, 2013
Homework
Prepare for Friday's
Probability Quiz
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11. Attachments
Develop a probability model.doc
Day 12 Theoretical Probability.pdf