I talk from time to time here about inference and probability. I'm reading Bernoulli's Fallacy, by Aubrey Clayton, which is a deep re-examination of the conventional way of doing scientific inference. It's too complicated and too profound for me to do a blog post right now -- I have talked about some of these problems before -- but early on he mentions the Monty Hall problem so just for fun, I'll present it here. Many people know it have learned what the answer is, but still have a hard time understanding it. Marilyn vos Savant, who billed herself as the smartest person in the world (hint: not) presented it in Parade Magazine many years ago, with the correct answer, and got bags full of hate mail from Ph.D. statistics professors who thought she was crazy.
If you're old enough to remember the daytime TV show Let's Make a Deal, host Monty Hall would present a contestant with three doors. Behind one was a fabulous prize, such as a new car, and behind two of them were joke prizes such as a goat or a free trip to Philadelphia. You had to pick one, then Monty would show you the joke prize behind one of the doors and ask if you wanted to switch your original guess. The question is, should you switch?
The Ph.D. statistics professors said it doesn't matter, you had a 1 out of 3 chance of picking the right door the first time and your chance is still 1 out of 3. Marilyn said you should switch. She was right. Why?
1 comment:
I mean ... once you've been shown a prize, isn't the probability no longer one out of three? But I'm missing the point here ...
In addition, if you've been given the goat ... it's obvious you'd do well to switch.
But what if you've been given the trip to Philly ... and you happen to be a U.S. history buff who likes cheesesteaks and wants to see where Franklin lived and worked after her moved there from Beantown?
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