Solution to The Impossible Bet
This problem is called the "100 Prisoners Problem", more info on the math here: http://en.m.wikipedia.org/wiki/100_prisoners_problem Thanks to http://www.ifixit.com for supporting us on Subbable!...
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Ok, so you remember the setup: 100 people have had marked dollar bills put randomlyinto 100 boxes, and every person, one at a time, gets to look in fifty of the boxes,and you all collectively win only if every single person finds their own bill. $100 dollarpayout to each of you if you win, nothing if you lose. In the last video I asked whetheror not you should take the bet.Did you make the right choice?I mean, clearly, if all 100 of you gamblers just choose 50 boxes at random when you gointo the room, the likelihood of each of you finding your bill is one half, so the probabilityof ALL of you finding your bills and winning the whole game is one half times one halftimes one half… a hundred times. And one half to the power of 100 is about 0.00000000000000000000000...
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Ok, so you remember the setup: 100 people have had marked dollar bills put randomlyinto 100 boxes, and every person, one at a time, gets to look in fifty of the boxes,and you all collectively win only if every single person finds their own bill. $100 dollarpayout to each of you if you win, nothing if you lose. In the last video I asked whetheror not you should take the bet.Did you make the right choice?I mean, clearly, if all 100 of you gamblers just choose 50 boxes at random when you gointo the room, the likelihood of each of you finding your bill is one half, so the probabilityof ALL of you finding your bills and winning the whole game is one half times one halftimes one half… a hundred times. And one half to the power of 100 is about 0.00000000000000000000000...
