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Wheel of Probability

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Wheel of Probability

Bernard Brooks

youtube link

- 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

- 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

- Why isn’t 1 a prime number?

- 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?

- Prime numbers
- Sieve of Eurastonese

- Fibonacci numbers
- Trees and pineapples

- Squares
- Triangle numbers
- Sum of 1 to n

- Perfect numbers

- 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

- 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

- 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

- Coin flipping
- Stock prices
- Yes/no questions
- Binomial probability
- Random social networks
- Pascal’s Triangle
- Binomial Coefficients

- 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?