18. Odds and Probability

Part One: Pascal's Triangle

• • Different Patterns found therein

  • Binomial Distribution (x+y)^n

  • Plinko

    • http://www.personal.psu.edu/dpl14/java/probability/plinko/

  • Flipping a coin

    • OUTCOMES may overlap, but the PATTERNS are unique

Part Two: Expected Value

• • Sample Space with one die

    • Probability with one die

  • Sample Space with two die

    • Probability with two die

bins=c(0.9,1.9,2.9,3.9,4.9,5.9,6.9,7.9,8.9,9.9,10.9,11.9,12.9)

diceroll=c() #sum of two regular dice

for(i in 1:10000){diceroll<-c(diceroll,sum(sample(1:6,2,replace=TRUE)))}

hist(diceroll,breaks=bins,col=rgb(1,0,0,1/2))

diceroll.12=c() #this is for a 12 sided die

for(i in 1:10000){diceroll.12<-c(diceroll.12,sample(1:12,1))}

hist(diceroll.12,breaks=bins,col=rgb(0,0,1,1/4),add=T)

Part Three: Expected Value

• • What type of game would make sense...and at what costs?

  • Can you beat the house?

  • POWERBALL.