It’s been a big week for fiction this week at Asparagus Pee – after racing through Life of Pi so The Lady Janet (fka Mrs. Asparagus Pee) could return it to the library on time, I’ve just finished The Curious Incident of the Dog in the Night-time, and I recommend them both highly.
Truth be told, there’s a little nonfiction hiding in them as well. In The Curious Incident, for instance, he has a detailed description of what is known as “The Monty Hall Problem.”
The set-up is, you are offered a choice of three doors. One door contains a prize, and the other two doors contain livestock. After you’ve chosen, Monty Hall opens one of the two doors that you didn’t pick to show that it contains a goat, and offers you a chance to pick the other door. The question is, are you better off to switch to the other door or keep your original choice, and the answer is very counterintuitive: you double your chance of getting the prize by switching every time. The intuitive answer, of course, is that it doesn’t matter because having one wrong door revealed makes it a 50/50 chance.
I’ve spent way too much time thinking about this, and I still have a hard time convincing myself, but I do believe you have a 1/3 chance if you stick, and 2/3 if you switch, which is the answer. There’s lots of good sites, some with simulation applets: Monty Hall Listings on Google.