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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?

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  • $\begingroup$ 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!) $\endgroup$
    – Nick Stauner
    Jul 31, 2014 at 1:25

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P(run into the person at least once) + P(run into the person never) = 1

That is, you either run into the person at least once, or you never run into the person at all.

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 $(1-.0625)^{12}$.

So,

P(run into the person at least once) = 1 - P(run into the person at least once) = $1-(1-.0625)^{12}$.

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