A very simple question, I think.

[st@ts]

Hi. I have what I think will be an easy question. Apologies if it's too trivial or if this is the wrong forum, I've never done stats, and really only signed up to ask this one question.

I've been told that, based on historical data, if I try X I have a certain probability of success (say 30%). How many separate times should I try X to give myself a probability (say 80%) of a single success?

I hope that makes sense. I'm not looking for a numeric answer, more an understanding of what type of problem this is, and how I can calculate them myself.

Thanks.
- st@ts.

[Etienne]

Hi,

Let p be the probability of success and Y the number of separate times one must try to obtain the first success :

P(Y = 1) = p

The event "you obtain the first success after k times" means "no success for k-1 times" and "sucess at the k-th try". Therefore :

P(Y = k) = p*(1-p)^(k-1)

Finally if you want P(Y = k) = 0.8, just solve for k this equation.

[BGM]

If you mean you want to have the first success on or before k times,
then probability you are looking for ?

[st@ts]

My thanks to Etienne and BGM. My results are:

P(Y=1) = 35.00%
P(Y<=2) = 57.75%
P(Y<=3) = 72.54%
P(Y<=4) = 82.15%
P(Y<=5) = 88.40%
P(Y<=6) = 92.46%
P(Y<=7) = 95.10%

FYI, the 35% represents the probability of a single live birth following the implantation of 2 embryos, as advised by a fertility clinic.