# Number of events to achieve a certainty

Apologies for this simple question, I'm sure it's been asked before, but I'm rusty on basic probabilities and my knowledge of terminology is long gone!

An event can be a pass or a fail. It always has 0.29 chance of passing, P. I want to know to get a given certainty X, how many events, N, it would take to achieve a given M successful events.

Sorry, I hope that's clear. So I have P, X and M, I would like to know N.

A walk through of an example would be very helpful.

Thanks

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This is binomial distribution. Suppose an experiment consists of $N$ trials and results in $M$ successes. If the probability on an individual trial is $P$, then the binomial distribution is: $$Bin(M;N,P) = C(N,M){P^M}{(1 - P)^{N - M}}$$ where $$C(N,M) = \frac{{N!}}{{M!\left( {N - M} \right)!}}$$ and I presume $X = Bin(M;N,P)$.
I forgot to mention that if you seek $N$ you need to use all the given information and try to solve for $N$. –  glebovg Oct 29 '12 at 4:51