Probability chosen according to a uniform distribution I read my book and find this "Let us now suppose that whereas the trials all have the same success probability p, its value is not predetermined but is chosen according to a uniform distribution on $(0,1)$", but I cannot see what really mean... any help, Thanks!

In the first case, $p$ is some deterministic value that you chose before (or that is determined by something). For example, you flip a coin, $p=0.5$. Then you have your $n$ trials, each having a probability $p$ of success.

In the second case, $p$ is now a random variable.

**First step** : draw a random number uniformly in $(0,1)$. This number, call it $p$. It may be any number in $(0,1)$ but now you know what it is.

**Second step** : do your trials, each having a probability $p$ of success. The same $p$ that was drawn at random before.

So in the second case there are two levels of randomness.

* The choice of the parameter $p$ is itself random
* The results of the trials are random