How To Calculate Binomial Distribution Of Really Small %? 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:
=1-BINOM.DIST(0,????,2^-160,TRUE)
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%=1-BINOM.DIST(0,229,0.01,TRUE)

*69 trials needed for 50%,  | 50.01%=1-BINOM.DIST(0,69,0.01,TRUE)

*1 trial needed for 1%,  | 1.00%=1-BINOM.DIST(0,1,0.01,TRUE)

Using manual tinkering with R I get the following values 
pbinom(0,3.365231884e48,2^(-160), FALSE)   = 0.9000000000339017
pbinom(0,1.0130357393e48,2^(-160), FALSE)  = 0.5000000000001161
pbinom(0,1.46885823057e46,2^(-160), FALSE) = 0.01000000000005571

As a check 
pbinom(0,229,0.01, FALSE) = 0.8998941257385102
pbinom(0,69,0.01, FALSE)  = 0.5001629701008011
pbinom(0,1,0.01, FALSE)   = 0.01

