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Total number of trials = N. The trials are independent. Probability of success = p. Probability of failure = 1-p. What would be probability of getting m or more consecutive successes?

Is there some online/downloadable efficient software where I can input N, m, p and it gives me the answer? Can scientific calculators can do this job?

kpv
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  • see this answer which gives you an immediate solution –  Aug 16 '16 at 01:31
  • @Igael: my numbers are big, are there any online tools, or scientific calculators that can do this for me? – kpv Aug 16 '16 at 03:03
  • @Igael: My N is more than 877 million and m is between 79000 and 80000 – kpv Aug 16 '16 at 04:57
  • because 80000, expect almost 0 ! the billion doesn't change a lot. An algorithm may be optimized. For stackoverflow ? I'll try to compute tomorrow how many trillions of random checks are needed to expect to find this sequence 1 time with 50% of chances ( it's a reverse of a googol at 99.99% ) –  Aug 16 '16 at 05:18
  • @Igael:The probability of success is very very high (6204/6205). which is .0.999838839645447.... Therefore, I do not expect it to be 0. Let me give you exact numbers then, N = 877646440, m = 79279, p(success) = 6204/6205. I want to know expected number of 79279 or more consecutive successes. – kpv Aug 16 '16 at 05:40
  • I bet 1 quarter of point on this result ! ( follow the first link to the answer for an estimation at the end of the post ) –  Aug 16 '16 at 05:57
  • @Igael: as that question is slightly different (it may be same but described little different), if you can give me the formula here in terms of N, m, p, then I can calculate the approximation. – kpv Aug 16 '16 at 06:04
  • there is an upper bound of $N 2^{-m}$ and never $6204/6205$. Ask a question on stackoverflow and send me a comment to help you to write the matrix script –  Aug 16 '16 at 20:51

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