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# Wheel of Probability - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Wheel of Probability' - metea

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Presentation Transcript

### Wheel of Probability

Bernard Brooks

• 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

Sieve of Eratosthenes

• 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

• 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?