Image via WikipediaHow many coins need to be released so that chances are that one coin will make it all the way down the slide?
Friday, November 12, 2010
Sliding Coins
Image via WikipediaHow many coins need to be released so that chances are that one coin will make it all the way down the slide?
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Chances for a coin to get past the first hole are 1:2, chances to pass the second hole are then 1:2 x 1:2 = 1:4, and finally chances to pass the third hole are 1:4 x 1:2 = 1:8.
ReplyDeleteWe should release 8 coins and theoretically one of them should make it all the way down.
Why do I get a feeling it can't be that simple?
Hmmm.... I think it depends how you interpret "...the chances are...".
ReplyDeleteFor example, with seven roles there is a 39% chance (i.e (7/8)^7) that no coins would make and, therefore, a 61% (1-0.39) that at least one coin would make it. So the chances are that at least one coin would make it.
Similarly, for 6 coins there is a 45% that no coins will make it and a 55% chance that at least one will. So, agian, the chances are that at least one coin would make it.
1 coin
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