I asked this question on the Bitcoin Forum, but I think it's more appropriate for a mathematics forum.
I'm making an informative video and I need a binomial distribution calculation. I want to find out how many trials are needed to get 1%, 50% and 90% likelihood 1 or more successes. The problem is that the likelihood of success is 1 out of 2^160 (number of distinct bitcoin/ethereum addresses).
Normally for something like this, I would use a binomial distribution calculation in Excel using this formula:
I would then tinker with the
???? until the entire cell result returned 1%, 50% and 90%. However, Excel can't handle numbers anywhere near this large. Does anyone know of a way I can calculate the number of trials required for these 3 percentages given the infinitesimally small chance of success? It would be great if there was an online tool I could use to support my results.
Just to illustrate what I'm looking for. If this analysis was for something much simpler, such as a probability of success being
1%, then I could calculate the results to be:
- 229 trials needed for 90%, | 89.99%
- 69 trials needed for 50%, | 50.01%
- 1 trial needed for 1%, | 1.00%