Calculating average from probabilistic measurements?

[mkbh_10]

I have got a sample size of 1000 and I calculated the mean probability of success of an event by breaking this sample size into sets of 50 and also have the standard deviation and standard error of mean of this success.

Now I repeat this process and have another set of data.

What will be the process of calculating the average of the probability and the error?

 

[Simon Bridge]

The setup is:
You have done an experiment of n(=50) identical trials which you repeat m(=20) times getting N=nm(=1000) trials.
In each experiment you have s successes, so the probability of a success in each experiment is estimated as: p=s/n or something like that?
This gives you n slightly different values for p - a "distribution" - from which you can find a mean and a standard deviation.

You do this again ... getting another mean and standard deviation from the new distribution of p values.

Now you are wondering how to combine the two distributions?
That about it?