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Clyde Oliver wrote at 2014-06-02 21:38:47

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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##### Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

##### Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0