# Trying to figure out a formula and answer to probability question

If I go to a certain establishment 12 times in one year (let's just say once a month), and there's a 6.25% chance each time that I go in there that I would run into a person I know, what is the probability that I would run into a person I know at least one time during the course of those 12 occurrences?

Can you tell me the probability and exactly how you derived that answer?

• If applicable, see the self-study tag wiki. (I'm guessing you're not just asking out of curiosity, but if you are, more power to you!) – Nick Stauner Jul 31 '14 at 1:25

P(run into the person never) = $(1-.0625)^{12}$
That is, the chance that you don't run into the person during a given visit is (1-.0625). The chance that you don't run into the person in any one of those 12 visits is $(1-.0625)^{12}$.
P(run into the person at least once) = 1 - P(run into the person at least once) = $1-(1-.0625)^{12}$.