Three years ago Anna and I went to Virginia for Christmas. We were reading Marilyn vos Savant and her explanation of what is known as the Monty Hall problem. I was astounded by it. So much so that we recreated it in the living room and found that it was real. I present it to you now in my own version:
Suppose you are on a game show and there are three doors. Behind each door is a prize. There is a Hostess orange cupcake behind one of the doors and Vomit Bertie Bott's Every Flavor Jelly Beans behind the other two doors.
You are told to pick one of the three doors, which you do. Instead of opening that door, the game show host (who knows what is behind each of the three doors) opens one of the other two doors; one that has a jelly bean behind it. You are left with two doors and instructions to make another choice. You may chose your original door or the other closed door. Should you stick with your original choice or switch?
Which would you do?
You should switch. Your odds have changed. You should switch and have your odds increased.
When you picked the first time, you had a 1/3 chance of getting the door with the cupcake. After the host opens up a jelly bean door, everything changes. If you stick with your original pick, you still have only a 33% chance of getting the cupcake even though it seems like nothing should change.
If you switch doors, your odds shoot to 66%. You will get the cupcake 2/3 of the time if you switch.
In other words, there is a 66% probability that the first door you pointed at was a barf bean. When the other bean is revealed, you should switch to the door that now has a 66% probability of hiding the cupcake.
Cool, huh?
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7 comments:
Man, that Hostess cupcake sure looked good. I wish I had some chicken nuggets right now. Sigh.
Oh, that last comment was from me, Anna. I didn't sign out of Chris's account. He doesn't much care for chicken nuggets.
Anna, here is your prize:
http://dcsleez.com/wp-content/uploads/2009/03/chicken_mcnuggets.jpg
That Hostess cupcake does look really good.
I remember that Christmas. I think we had a family activity where we all tried it out and kept tally. It really is true. In a freaky way. Like alternate universe.
WEIRD. I don't know if I believe you.
This is too weird for me to believe. The probability CHANGES when the guy opens the door?? But wouldn't you have the same...? I don't know.
It just seems to me that after he opens the other door that you now have a 50-50 chance of getting it right, not a 66-33.
OK, I think I understand it now. Imagine that instead of three doors there are 100 doors, with the cupcake behind one and 99 vomit beans all the rest. You choose one door and the guy opens 98 other doors. You can either switch to the closed door or you can stay with your first choice. I think most people would switch in that circumstance.
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