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I got the following thought out of the book I'm currently reading, Sixty Days and Counting -
You start off with three boxes, one of which contains a ten pound note. The boxes are all closed. You choose one box, and get to hold on to it (still closed). Of the two boxes left, the dealer opens an empty box. You can then choose to swap boxes or not. What should you do?
Now, to me, this was a straight 50-50 - the note is either your box, or the other box. However, there's another answer given -
Each box has a 1/3 chance of containing the tenner. Therefore, when you choose your box, it has a 1/3 chance, and the other two boxes have a combined likelihood of 2/3 chance. So far so good. However, once you open the empty box, the probability doesn't drop... so you have 2/3 probability concentrated in the other box, versus the 1/3 in your own box. You should always therefore switch.
Now... this makes sense. However, I think there's a fallacy in there somewhere. Does opening up one of the boxes constitute an outside event that means you are at a new event nodule and have to recalc probabilities again? Or is the above argument correct, and you are still in the same event?
You start off with three boxes, one of which contains a ten pound note. The boxes are all closed. You choose one box, and get to hold on to it (still closed). Of the two boxes left, the dealer opens an empty box. You can then choose to swap boxes or not. What should you do?
Now, to me, this was a straight 50-50 - the note is either your box, or the other box. However, there's another answer given -
Each box has a 1/3 chance of containing the tenner. Therefore, when you choose your box, it has a 1/3 chance, and the other two boxes have a combined likelihood of 2/3 chance. So far so good. However, once you open the empty box, the probability doesn't drop... so you have 2/3 probability concentrated in the other box, versus the 1/3 in your own box. You should always therefore switch.
Now... this makes sense. However, I think there's a fallacy in there somewhere. Does opening up one of the boxes constitute an outside event that means you are at a new event nodule and have to recalc probabilities again? Or is the above argument correct, and you are still in the same event?
