Expectation value for first success in a binomial distribution?

[pellman]

This is not a homework problem. Just a curiosity. But my statistics is way rusty.

Suppose a binomial probability distribution with probability p for a success. What is the expected number of trials one would have to make to get your first success? In practice, this means if we took a large number of samples where we stopped at the first success and wrote down the number of trials N to get that success, what is the mean value of N?

 

[PeroK]

The answer is 1/p.

There's a very clever way to work this out here:

https://www.physicsforums.com/showthread.php?t=733925