The Monty Hall Problem

Ask Marilyn

This problem has an interesting history related to Marilyn vos Savant.

Simulating Monty Hall

n <- 1e4
simlist <- rep(NA, n)

for(i in 1:n) {                                # Replicate
  doors <- sample(c("goat", "goat", "car"), 3) # randomly distribute prizes
  choice <- sample(1:3, 1)                     # randomly choose door number (Simulate)
  if(doors[choice] == "car") {                 # if you chose the car
    opens <- sample(c(1:3)[-choice], 1)        # host will open one of the two goats
  } else {                                     # he will have to open the other goat
    opens <- setdiff(which(doors == "goat"), choice)           
  }
  final <- setdiff(1:3, c(choice, opens))
  simlist[i] <- doors[final]                   # Success?
}

sum(simlist == "car")/n                        # Estimate

## [1] 0.6702

Simulating the die roll

simlist <- sample(1:6, 1e5, replace = TRUE)
mean(simlist == 3)

## [1] 0.16709

oddsimlist <- simlist[simlist %in% c(1, 3, 5)]
mean(oddsimlist == 3)

## [1] 0.3331937