Advanced Math/Infinity

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Clyde Oliver wrote at 2014-06-02 21:38:47
You call this an answer?



The probability of winning each round is not zero, it is 1/10^10.



Out of the 10^10 ten-digit numbers, one of them is the winner.



So the probability of losing each round is 1 - 1/10^10.



The probability that you guess N times and get it wrong every single time is (1-1/10^10)^N.



So the probability that you get it right even once is:



1-(1-1/10^10)^N



As N grows larger, this quantity approaches 1. This means that over time, as the number of guesses goes to infinity, the "guesser" will actually win the game with probability 1 (i.e. probabilistic certainty).


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