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Martin-2 comments on Bayes' Theorem Illustrated (My Way) - Less Wrong

126 Post author: komponisto 03 June 2010 04:40AM

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Comment author: Martin-2 14 February 2013 04:32:33AM *  0 points [-]

Although it's late, I'd like to say that XiXiDu's approach deserves more credit and I think it would have helped me back when I didn't understand this problem. Eliezer's Bayes' Theorem post cites the percentage of doctors who get the breast cancer problem right when it's presented in different but mathematically equivalent forms. The doctors (and I) had an easier time when the problem was presented with quantities (100 out of 10,000 women) than with explicit probabilities (1% of women).

Likewise, thinking about a large number of trials can make the notion of probability easier to visualize in the Monty Hall problem. That's because running those trials and counting your winnings looks like something. The percent chance of winning once does not look like anything. Introducing the competitor was also a great touch since now the cars I don't win are easy to visualize too; that smug bastard has them!

Or you know what? Maybe none of that visualization stuff mattered. Maybe the key sentence is "[Candidate] A always stays with his first choice". If you commit to a certain door then you might as well wear a blindfold from that point forward. Then Monty can open all 3 doors if he likes and it won't bring your chances any closer to 1/2.