Monty Hall Problem: Simulation

Assume you choose door #1 as above.

num_samples = 10000
monty_1 <- dplyr::tibble(
   door_with_prize = sample(c(1,2,3), num_samples, replace = TRUE),
   door_monte_opens = dplyr::case_when(
                          door_with_prize == 1 ~ sample(c(2,3), num_samples, replace = TRUE),
                          door_with_prize == 2 ~ 3,
                          door_with_prize == 3 ~ 2)
)

Now condition on the observation “Monty opens door 2”:

monty_1 |>
  dplyr::filter(door_monte_opens == 2) |>
  dplyr::summarize(mean(door_with_prize == 1))

## # A tibble: 1 × 1
##   `mean(door_with_prize == 1)`
##                          <dbl>
## 1                        0.344