bigjeff5 comments on Bayes' Theorem Illustrated (My Way) - Less Wrong

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

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Comment author: Jiro 22 December 2013 04:24:10AM 0 points [-]

Here is the breakdown for the Boy1Tu/Boy2Any option:

Boy1Tu/Boy2Tuesda

Then the BAny/Boy1Tu option:

Boy2Tuesday/Boy1Tu

You're double-counting the case where both boys are born on Tuesday, just like they said.

A key insight that should have triggered their intuition that their method was wrong was that they state that if you can find a trait rarer than being born on Tuesday, like say being born on the 27th of October, then you'll approach 50% probability.

If you find a trait rarer than being born on Tuesday, the double-counting is a smaller percentage of the scenarios, so being closer to 50% is expected.

Comment author: bigjeff5 22 December 2013 04:48:30AM *  0 points [-]

Which boy did I count twice?

Edit:

BAny/Boy1Tu in the above quote should be Boy2Any/Boy1Tu.

You could re-label boy1 and boy2 to be cat and dog and it won't change the probabilities - that would be CatTu/DogAny.

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