Transcript Green Jawbreaker - lenny-prob

What,
A Green
Jawbreaker???
Probability and Statistics
Intuitively Accessible
Mathematically Complex
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Directly influenced by our everyday lives
Lotteries Prizes
500 year floods
Research related to what to eat,
environmental conditions
• Polls and elections
Probabilistic Thinking
• Transition from ordinary language to more
precise mathematical meanings.
• Students need to reason probabilistically
about data rather than simply to provide
answers to questions.
• Reasoning about the relationship between
data and probability.
Why Study Probability
• Chance is all around us—we do not live in
a totally deterministic world.
• In your group talk about how probability is
used in your world.
Why Learn About Probability
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Insurance
Disease/medical treatments
Genetics
Weather
Athletics
Gamble (responsibly)
Doing or not doing homework
Retirement/investments
Uses of Probability
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Genetics
Weather
Medicine
Insurance
Disease and health care
Gambling
Investments and retirement
Athletics
Doing or not doing assignment
Driving above the posted speed limit
We Must Teach Probability
• Do you purchase an item based on
consumer reports or the experience of one
friend?
• We must make decisions in the face of
uncertainty on a daily basis.
• Life changing decision can have a
foundation in probability and statistics.
• Our goal must be to develop students who
can make informed decisions.
A Green Jawbreaker???
• In the sack on your table you have 10
jawbreakers.
• Do Not Look or Open Sack Unless
Directed
• Your task, after collecting some data, will
be to guess the number of each color in
your sack.
Define Probability
• But before we begin in your group define
probability.
chance of success
Pr obability 
total in sample space
Let the Data Collection Begin
• Have someone in your group reach in the
sack without looking
– Pull out a jawbreaker
– Look at the color
– Put the jawbreaker back in the sack
– Record the observation on the flip chart.
• Is your group ready to take an estimate
(not guess) as to the contents?
• Repeat the above procedure.
Probability Concepts
• Notation for probability of an event.
– P(event) or P(A) =
• P(event) = 0
• P(event) = 1
• Can the probability of an event ever be
greater than 1? Why
• 0 < P(event) < 1
More Data
• Repeat the drawing procedure.
• Repeat the drawing procedure.
• Any surprises? Are you ready to
estimate?
Probability Thoughts
• If you flip a coin 4 times and get 4 heads,
what is the probability of getting heads on
the 5th toss?
• What if you flip a coin 15 times and get 15
heads?
• If you flip a coin 100 times will you get 50
heads and 50 tails.
• State the law of large numbers in your own
words.
More Probability
• All events in an experiment must have an
equal chance of occurring. Could we use
coins in our sack? A clear sack?
• The sum of the probabilities of all possible
events will equal what?
• P(NA) is the probability of A not occurring.
This is called the complement of an event.
• If the P(A) = ¼ what is the P(NA)?
• Birthday problem example
More Data
• Repeat the drawing procedure.
• Are you ready to guess now?
• Repeat the drawing procedure one more
time.
• How many would you need to draw to
have a good idea of what is in your sack?
• To be 100% sure.
• Nothing is certain in probability.
Here We Go
• If you correctly estimate the contents of
your sack you will get a jawbreaker.
• Full disclosure—I do not know how many
are in each sack.
Extension Activity
• Fill three sacks with jaw breakers, 8 red
and 12 blue, 12 red and 8 blue, 3 red and
17 blue.
• Tell the students that you forgot which is
which.
• Take one of the sacks and draw one at a
time and replace. Repeat several times
and have them decide which mixture has
been chosen.
Finishing Up
• Go to another sack and repeat the
process.
• Go to the last sack and repeat.
• Allow them to change their guess and
make sure that they justify their selections.
Probability Questions
• Which is most likely to happen
– Get more than 7 heads out of 10 tosses
– or more than 70 heads out of 100 tosses?
• In a family of 4 children is it more likely to
have BBBB or BBGG?
Other Activities
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Toss a tack, what could happen
Toss a styrofoam cup.
Spin a coin rather than toss
This requires a large number of trials
In Angel there is a file Green Jawbreaker
which contain reference to this activity.