factorial(4)

choose(7,4)

1/128*35


choose(7,0:7)

choose(7,0:7)/128

sum(choose(7,0:7)/128)

barplot(choose(7,0:7)/128)

barplot(choose(7,0:7)/128,ylab="Probability",xlab="Heads",names = as.character(0:7))

choose(49,6)

choose(49,6)*20/(60*60*24*365)

factorial(52)/(factorial(13)^4)

factorial(4)*(factorial(48)/(factorial(12)^4)) /(factorial(52)/(factorial(13)^4))

0.9^6*0.1

sum(0.1*0.9^(0:6))

x<-runif(100000)
theta<-2*pi*runif(100000)
left<- ifelse (x<0.5,x-0.5*abs(cos(theta)),0)
right<- ifelse (x>=0.5,x+0.5*abs(cos(theta)),0)
p<-(sum(left<0)+sum(right>1))/100000
p

2/p

pi

ceiling(6*runif(1))

sum(ceiling(6*runif(3)))

total<-numeric(1000)
for (i in 1:1000) total[i]<-sum(ceiling(6*runif(3))) 
hist(total)

p<-c(1/4,1/6,1/8)
d<-c(22,11,15.25)
plot(p,d,type="l")

