Simulated experience #2

There are 3 doors.

Behind one of them is a Ferrari of your favorite color.

You do not know which door is the winner.You don’t.

But I do!

I ask you to select a door and you make a choice.

Once you choose a door, I eliminate one of the two that you did not select, while making sure that there is NO Ferrari behind the door I eliminate.

Now…

Do you stay with your original choice, or given the option, would you change to the other remaining door?

This is the famous Monty Hall problem. And it confuses a lot of people.

The probabilistic structure, like in the birthday problem, is hard to understand.

Although one might be inclined to think that the odds are 50%-50% at the last stage, it turns out that if you change doors, your chances of getting that Ferrari is 67%, and if you stay, it is only 33%.

There is, of course, an analytic solution to this problem. But why bother? Use simulated experience. Just take 3 playing cards, 2 black and 1 red (Ferrari).

Put them upside down as you make a selection. Then, turn them over, take out a black card out of the ones that you did not select and make a note of the result. You’ll see that when you repeat this procedure over and over again, out of the remaining cards, the red one will mostly be the other card.

Or, play the game HERE.