Wheel of Probability Bernard Brooks youtube link Wheel

Wheel of Probability Bernard Brooks youtube link

Wheel of Probability • Probability and number types • http: //mathmidway. org/Training/pdf/numberline. Tour. Guide. pdf • Number Devil book • How many primes from 1 -100: • Sieve of Eratosthenes • Binomial Tree and coin flipping

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 • Why isn’t 1 a prime number?

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

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 •

Excel Plot of Binomial Tree 10 8 6 4 2 0 1 -2 -4 -6 2 3 4 5 6 7 8 9 10 11 12 13

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

Questions?

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?