Question

Using Rstudio

# 1. Monty-Hall Three doors

Recall the Monty-Hall game with three doors, discussed in class. Run a simulation to check that the probablility of winning increases to 2/3 if we switch doors at step two.

Set up the experiment two functions "monty_3doors_noswitch" and "monty_3doors_switch" (these functions will have no input values):

```{r}
monty_3doors_noswitch <- function(){
  
}

monty_3doors_switch <- function(){
  
}

```

Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
Compare your answers with the actual theoretical predictions.

```{r}

```

Answer 1

monty3doors_no_switch.r:

monty3doors_no_switch <- function(){
  
doors = c(1,2,3) # had 3 doors
  
ch1 = sample(doors, 1) # 1st choice: pick one door at random
crct1 = sample(doors, 1) # the correct box
  
# Assume When making the second choice, you stick with the original choice and you are RIGHT
  
# let X be a binary variable that takes the value 1 if the choice is correct and 0 if incorrect
x = 0
x = ifelse(ch1 == crct1,1,0) # you stick with the original choice and you are RIGHT
x
}

no_of_Successes = replicate(1000000, monty3doors_no_switch())
prob = sum(no_of_Successes)/1000000
probability = prob
probability

Output Screenshot:

monty_3doors_switch.r:

monty_3doors_switch = function(){
  
doors = c(1,2,3) # had 3 doors
  
ch = sample(doors, 1) # 1st choice: pick one door at random
crct = sample(doors, 1) # the correct box
  
# When making the second choice, you stick with the original choice and you are WRONG.
  
# let X be a binary variable that takes the value 1 if the choice is correct and 0 if incorrect
x = 0
x = ifelse(ch != crct,1,0) # you stick with the original choice and you are WRONG.
x
}

no_of_Successes = replicate(1000000, monty_3doors_switch())
prob = sum(no_of_Successes)/1000000
probabilty = prob
prob

Output Screenshot:

Compare your answers with the actual theoretical predictions: