On Sun, Feb 26, 2012 at 7:57 PM, Charles Greathouse <charles.greathouse@case.edu> wrote:
Well, you can determine the probability for 1 through 9 directly, to wit 1 1/9 2 10/81 3 100/729 4 1000/6561 5 10000/59049 6 100000/531441 7 1000000/4782969 8 10000000/43046721 9 100000000/387420489
Then you can set up the linear recurrence and solve for the coefficients. The coefficient of the power of 1 should give the answer, since all other roots of the characteristic polynomial have absolute value < 0.805 and so are insignificant for the "arbitrarily large" positive integer you start at.
Or you can just realize that since on average you are subtracting 5, about a fifth of the numbers will be in the sequence, so the probability that 0 is in the sequence is about 1/5. Andy
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Sun, Feb 26, 2012 at 7:21 PM, Hans Havermann <gladhobo@teksavvy.com> wrote:
Begin with some arbitrarily large positive integer and repeatedly subtract a randomly chosen integer from zero to nine. What is the probability that you will land on zero?
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