In a game (XCOM) you have a stated chance of hitting the target. You either hit or miss. Let's say your chance of hitting is 90% every time.
I want to know the chance of 3 misses (10% each) happening 3 times in a row anywhere given n trials (let's say 50, 100, 200 etc)
Ideally I'm looking for a simple solution, and it can be an approximation.
The only way I can think is working out permutations for each possible number of misses (probability of x number of misses calculated from binomial formula) but that would take quite a long time. I'm wondering if there's a more elegant way.
It would be also nice to know the probability of at least 1 such streak, at least 2 etc.