I would like to share with you one method for proving to yourself the results of the Monte Hall problem. There's something so difficult about describing the results of the Monte Hall problem that sometimes doing something physical like this will help show you why you get the results that you get. In this case we're going to use some playing cards to represent the three doors. You can use slips of paper which I've done before where you've written Goat and Car on them. The slips of paper just get to be a little bit difficult to handle. The cards are easy to shuffle and handle. In this case the cards are going to represent two goats and the car. And what we do is we're going to shuffle them. There's actually two random systems or random choices that are made in this system. We're just going to use the first one which is the producers randomizing where the car is behind the three doors. In this first run through we're going to pick the first door every time. Monte knows there's at least one goat behind the other two doors and shows this to us. And we're left with the two doors. An important point is to realize that this next step is not a random event. It's actually the conditions that we're testing for in this system. Meaning if I stayed with the first door when I get a go to a car, if I switched when I get a go to a car, in this case if I switched I would have gotten a car. We then repeat the system. We're going to do this 100 times and see what we get. Again we've randomized the cards. You do that until you're comfortable that that's random. Monte shows you one of the goats and we know there's a goat behind this door. So in this case again if I switched I would have gotten the car. If we do this 100 times you'll get your results. Here's a run that I made where if I stayed 29 out of 100 times or 29 percent I got the car. When I switched 71 out of 100 times or 71 percent I got a car. We expect 33 and 66. With a small set like this these numbers are close enough to prove what we're looking for. Now as I said there's actually two random events. This one is the producers placing the car behind the door. The second one is which door you choose. You only need one of those two random systems for this to work. The other way you can do this is to leave the car in the same place and use a die to randomize your choice. In this course one two three four five six I choose the first door. Monte shows us a goat and in this case if I switched I would have gotten the car. In this case I choose the middle door. Monte shows us the goat in this case again if I switched I would have gotten a car. This method is a little faster because you don't need to shuffle the cars. The important thing to choose here is the system that makes you feel that we're duplicating the conditions of this test. Has it's described. If those two aren't working you can use both of these together. You can randomize the car and randomize your choice. If that makes you feel that you've got the conditions and in the end we'll get the 29 or 33 66 percent and after you've done that we need to sit down and think about why it's a one third and two thirds probability is not 50 50.