### This is a program used to simulate rolling fair dice.
# Specify the number of dice to be rolled.
NumberOfDice <- 2
# Specify the sum you are interested in.
DesiredSum <- 7
# Simulate rolling dice.
SumOfRandomDice <- function(n){
	S <- 0
	for (i in 1:n){S <- S + trunc(6*runif(1)) + 1}
	return(S)
}
# 1.
# a.
Reps <- 100
Count <- 0
for(i in 1:Reps){
	if(SumOfRandomDice(NumberOfDice) == DesiredSum) Count <- Count + 1
}
Prob <- Count/Reps
cat("The count is", Count,"for",Reps,"rolls.","\n")	# \n give a <return>
cat("The probability of",DesiredSum,"for",NumberOfDice,"dice is", Prob,".\n")
# b.
Reps <- 1000
Count <- 0
for(i in 1:Reps){
        if(SumOfRandomDice(NumberOfDice) == DesiredSum) Count <- Count + 1
}
Prob <- Count/Reps
cat("The count is", Count,"for",Reps,"rolls.","\n")       # \n give a <return>
cat("The probability of",DesiredSum,"for",NumberOfDice,"dice is", Prob,".\n")
# c.
Reps <- 10000
Count <- 0
for(i in 1:Reps){
        if(SumOfRandomDice(NumberOfDice) == DesiredSum) Count <- Count + 1
}
Prob <- Count/Reps
cat("The count is", Count,"for",Reps,"rolls.","\n")       # \n give a <return>
cat("The probability of",DesiredSum,"for",NumberOfDice,"dice is", Prob,".\n")
# 2.
NumberOfDice <- 4
DesiredSum <- 14
Reps <- 10000
Count <- 0
for(i in 1:Reps){
        if(SumOfRandomDice(NumberOfDice) == DesiredSum) Count <- Count + 1
}
Prob <- Count/Reps
cat("The count is", Count,"for",Reps,"rolls.","\n")       # \n give a <return>
cat("The probability of",DesiredSum,"for",NumberOfDice,"dice is", Prob,".\n")