HW 2

x <- seq(1,6,1)
d1 <- expand.grid(x,x,x)
rowsum <- rowSums(d1)
sum(rowsum==12)/length(rowsum)

## [1] 0.1157407

The probability is 0.1157.

cust <- matrix(c(200,300,200,100,100,200,200,100,200,100),5,2,byrow = T)
(200+100)/sum(colSums(cust))

## [1] 0.1764706

The probability is 0.1765.

first <- 13/52
second <- (13/52)*(12/51)
second/first

## [1] 0.2352941

The probability is 0.2353.

#install.packages('gtools')
library(gtools)
factorial(20)/factorial(10)/factorial(10)

## [1] 184756

There are 184756 possible lineups.

choose(20,1)*choose(20,1)*choose(18,1)

## [1] 7200

There are 7200 choices

factorial(10)

## [1] 3628800

The doctor has 3628800 ways.

coin <- 2^7
die <- 6^3
card <- choose(52,4)
coin*die*card

## [1] 7485004800

There are 7485004800 outcomes.

factorial(4)*factorial(3)

## [1] 144

There are 144 ways.

10.

PAB <- 1/3
# PAB is P(AB)
PA<- 3/6
#PA is P(A)
Q10 <- PAB/PA
print(Q10)

## [1] 0.6666667

P(B|A) = P(AB)/P(A)

P(AB) = Take one pancake out after it has browned on both sides