The Monty Hall 'Let's Make A Deal' Problem


My son Zach introduced an interesting topic over lunch the other day. It's called the Monty Hall 'Let's Make A Deal' problem. If you remember the show, a contestant would be given a choice of three curtains. Behind one would be a new car. The other two curtains would each have nothing behind them. The contestant picks a curtain. Before Monty Hall would show them whether or not they won, he would pull open one of the two curtains that wasn't chosen to reveal that there was nothing behind it. Then Monty would ask, "would you like to stick with your original choice? Or would you like to choose the other remaining curtain?" Here's the question: Should you stick with your first pick or should you switch? Almost everyone sees this as a 50/50 scenario and says the odds are equal whether you stick with your initial pick or if you switch. Believe it or not, the math favors you making the switch to the curtain you had not chosen originally. In fact, your odds of winning with your initial pick were 1/3. Your odds of winning if you switch to the next curtain become 2/3. My son and I argued over this for quite a while with me coming down on the 50/50 odds side of the argument. But my son was right! The odds favor making the switch. Watch the video for the explanation.

And below, Monty Hall himself speaks about the problem.


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