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Wheel of Probability

Wheel of Probability. Bernard Brooks youtube link. 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 E ratosthenes Binomial Tree and coin flipping. Activities.

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Wheel of Probability

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  1. Wheel of Probability Bernard Brooks youtube link

  2. 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

  3. 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

  4. Sieve of Eratosthenes • Why isn’t 1 a prime number?

  5. 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?

  6. Number Names • Prime numbers • Sieve of Eurastonese • Fibonacci numbers • Trees and pineapples • Squares • Triangle numbers • Sum of 1 to n • Perfect numbers

  7. 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

  8. 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

  9. Excel Plot of Binomial Tree

  10. 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

  11. Simple Rules • Coin flipping • Stock prices • Yes/no questions • Binomial probability • Random social networks • Pascal’s Triangle • Binomial Coefficients

  12. Questions?

  13. 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?

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