# Monte Hall

reference:
- Monty Hall problem

### simulation: car or goat

``````pick <- function(n){
sample(c("car", "goat", "goat"), n, replace = TRUE)
}``````
``pick(10)``
``##  [1] "car"  "car"  "car"  "goat" "car"  "car"  "goat" "goat" "car"  "goat"``
``table(pick(1000))``
``````##
##  car goat
##  318  682``````

### simulation: 1 or 0

``````pick.1.0 <- function(n){
sample(c(1, 0, 0), n, replace = TRUE)
}``````
``pick.1.0(10)``
``##  [1] 0 0 0 0 1 0 0 1 0 0``
``table(pick.1.0(1000))``
``````##
##   0   1
## 664 336``````

### long-run probability

``````set.seed(2027)
n <- 1:1000
picks <- pick.1.0(1000)
cumsum.picks <- cumsum(picks)   # cummulative sum of picks
df <- data.frame(n, picks, cumsum.picks, p = cumsum.picks / n)
str(df)``````
``````## 'data.frame':    1000 obs. of  4 variables:
##  \$ n           : int  1 2 3 4 5 6 7 8 9 10 ...
##  \$ picks       : num  1 0 1 0 1 1 0 0 0 0 ...
##  \$ cumsum.picks: num  1 1 2 2 3 4 4 4 4 4 ...
##  \$ p           : num  1 0.5 0.667 0.5 0.6 ...``````
``````ggplot(df, aes(n, p)) +
geom_line(color = "skyblue") +
ylim(0, 1) +
geom_hline(yintercept = 1 / 3, color = "orange", lty = 2) +
labs(title = "Long-run Probability")``````