Part One: Pascal's Triangle
Different Patterns found therein
Binomial Distribution (x+y)^n
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
probability vs. sample space, and some good practice problems.
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.