Katie A. Larsell Portland, OR

Dear Tom and Ray:

What a surprise to know the answer to the puzzler. My husband is a mathematician, so when our kids do a science project for the science project for the science fair, they can't get away with displaying rocks they picked up at the beach. Poor kids! Our ten year old got to demonstrate the Monty Hall Problem at the last science fair. My son and I put together a little stage with three doors. We kept a running tally sheet of the discussions that were made. As people came by, we ran them through the problem and asked them if they wanted to switch doors. Actually, my husband and I did most of the demonstrating, since our son found a friend and they ran around looking for loose change so they could buy treats at the vending machine. But we know who these science projects are really for anyway!

After an evening with probably 50 people trying it out, the data sheet showed that it definitely paid to switch. Now you can explain it until you are blue in the face. For me it defies common sense--but it does work. (By the way, it is a probability problem. When you start out each door has a one third probability of being the prize, but as soon as you know that it's not in Monty's door then your door still has a one third probability of being the correct door, but now the other door has all the left-over probability. The probabilities have to add to one and so the probability of the other door having the prize is two thirds. Yes, know, it still doesn't sound likely. But it does work.

Sincerely,
Katie A. Larsell

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