Part One: 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)
What type of game would make sense...and at what costs?
Can you beat the house?
POWERBALL.
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Part Two: Pascal's Triangle
Different Patterns found therein
Binomial Distribution (x+y)^n
Plinko
Flipping a coin
OUTCOMES may overlap, but the PATTERNS are unique
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1. powerball: WHO WON????!!!!!
2. your games ... let's play them.
3. let's play one that was created a while back ... and extend it a little bit.
Activity Two: Flipping a Coin
we are going to get very different results here: some will get ten coin flips all heads, some tails, some of us near the center
but how do we know if it's a fair coin?
BIG IDEA: when we sample, we head towards the mean. But this means that there are going to be drastic differences. sometimes, when we sample, we are going to get a result that is off from what we expect.
What does it mean to sample?
Activity Two: Sampling from the M&M sheet
we are bad at picking out boxes on our own. We used r to get the boxes for us to select. This gave us better results than we had before.
Sampling from a sheet
convenience sampling
"random" sampling
random number table
randomness from the internet
sample 10 according to r. take those values and make a graph as a class: