Wheel of probability
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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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Wheel of probability

Wheel of Probability

Bernard Brooks

youtube link


Wheel of probability1

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


Activities

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


Sieve of eratosthenes

Sieve of Eratosthenes

  • Why isn’t 1 a prime number?


Exhibit prompts

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?


Number names

Number Names

  • Prime numbers

    • Sieve of Eurastonese

  • Fibonacci numbers

    • Trees and pineapples

  • Squares

  • Triangle numbers

    • Sum of 1 to n

  • Perfect numbers


Fibonacci tree

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


Binomial tree

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


Excel plot of binomial tree

Excel Plot of Binomial Tree


Social network

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


Simple rules

Simple Rules

  • Coin flipping

  • Stock prices

  • Yes/no questions

  • Binomial probability

  • Random social networks

  • Pascal’s Triangle

  • Binomial Coefficients


Questions

Questions?


Wheel of probability prompts

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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