This problem is shown on the video linked here [+] at 17 minutes 30 seconds into the video.

Here is the link to the Monti Hall simulation. 1. Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say door number 1 (but the door is not opened), and the host, who knows what's behind the doors, opens another door, say door number 3, which has a goat. He then says to you, "Do you want to pick door Number 2?"

Experimental Probability:

(a) Run the Monti Hall simulation 100 times where you DO NOT change your choice. What percentage of times do you win?

(b) Run the Monti Hall simulation 100 times where you DO change your choice. What percentage of times do you win?

Theoretical Probability:

(c) What is the theoretical probability of winning if you don't switch your choice? (d) What is the theoretical probability of winning if you do switch your choice? (e) Is it to your advantage to switch your choice? (Type either yes or no) 2. Suppose you're on a different game show. The host has you take a card from a deck of 52 playing cards. You don't know what card you picked because it is face down. You're suppose to guess the playing card you just picked. Let's say you guess the two of clubs. The host then shows you all the other cards in the deck except for one card. If he has the card you guessed, then he does not show you that card. If he doesn't have the card you guessed, then he still doesn't show you one card. He then says to you, "Do you want the card you originally picked or do you want to chose the card I have". (a) What is the probability you guessed the card if you don't switch your choice? (b) What is the probability you guessed the card if you do switch your choice? (c) Is it to your advantage to switch your choice? (Type either yes or no)