Talk:Argon Scope/@comment-73.234.131.123-20160129213037/@comment-76.126.115.28-20160131144240

Zxorn is right. This kind of thing is called a Bernoulli trial, where each round you have two outcomes with fixed likelihoods, success (4%) or failure (96%). Chance of 200 trials and no success is simple: P(no mod in 200 runs) = (96%)^200 * (4%)^0.

This kind of calculation is cool, because you can answer the question "How likely am I to get at least one Argon Scope in 25 runs?". (Because we know 25 runs is the expected value for a probability of 4%)

P(getting mod in 25 runs) = 1 - P( getting no mod in 25) = 1 - (96%)^25 * (4%)^0 = 1 - .96^25 = 1 - .36 = 0.64

64%, roughly 2 out of 3 chance of getting at least one.

Next time RNG bones you, check the math to put things in perspective.