Wheel of Probability
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Transcript of Wheel of Probability
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Wheel of ProbabilityBernard Brooksyoutube link
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Wheel of Probability• Probability and number types• http://mathmidway.org/Training/pdf/numberlineTourGuide.pdf • Number Devil book • How many primes from 1-100: • Sieve of Eratosthenes
• Binomial Tree and coin flipping
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Activities• Sieve of Eratosthenes• Fibonacci tree• Binomial tree• Betting: If I am selling a ticket that pays $10 if you spin an even
number and nothing if you get odd, how much is that ticket worth? • Hint: less than $5
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Sieve of Eratosthenes
• Why isn’t 1 a prime number?
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Exhibit Prompts• Probability of getting• Even number• Number less than 30• Triangle number (1,3,6,10,..)• Prime number
• Uniform distribution of one spin but take the average of spins and it approaches a Gaussian
• Betting on the wheel: What does a $1 wager that pays off if you spin a 29 have to pay to be a worthwhile bet?
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Number Names• Prime numbers• Sieve of Eurastonese
• Fibonacci numbers• Trees and pineapples
• Squares• Triangle numbers• Sum of 1 to n
• Perfect numbers
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Fibonacci Tree• What is the probability of getting a Fibonacci number?• Tree rule: a branch needs to mature before it can birth a new
off shoot. Start with a new shoot.
• Pine cones• Pineapples• Flowers
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Binomial Tree• Start the children all in a line (at 0 on a number line)• Odd: step forward, even backward • After 10 steps graph where everyone is: Gaussian curve• Prompts: what’s the farthest you can be? What is the chance that
happens?• What about the rule: 30 step back, > 30 step forward?• Can be done with coin flipping (10 coins at once)• Mean value or expected value of np• Variance as expected value of (x-np)2
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Excel Plot of Binomial Tree
1 2 3 4 5 6 7 8 9 10 11 12 13
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Social Network• Binomial Random Network• With 10 people how many connections are possible? (it’s a
triangle number)• With p=1/2, how many connections are expected?• Draw the degree distribution and see it’s Gaussian
• Preferential Attachment Network• Start with kite graph• Add people with 2 edges • Rich get richer
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Simple Rules • Coin flipping• Stock prices• Yes/no questions• Binomial probability• Random social networks• Pascal’s Triangle• Binomial Coefficients
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Questions?
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Wheel of Probability Prompts• What is the probability of getting• Even number• Number less than 30• Triangle number (1,3,6,10,..)• Prime number
• If we all spin the wheel once and graph the distribution of our results we get a uniform distribution. • If we spin 2 times and average them, 3 times and average, etc. it
approaches a Gaussian• What does a $1 wager that pays off if you spin a 29 have to pay
to be a worthwhile bet? • We see Fibonacci numbers in nature more often than chance
would dictate; why?