20% chance of seeing a person. what is expected number of trips to grocery store before you meet this person?

p = 0.2; q = 1 - p = 0.8

Let n be the number of trips before you meet this person.

Then P(n = 1) = p; P(n = 2) = q*p; P(n = 3) = q^2*p; P(n =4) = q^3*p, etc.

The expected number of trips is 1*p + 2q*p + 3q^2*p + ... = p/(1-q)^2 = p/p^2 = 1/p = 1/0.2 = 5

Answer: 5 days.

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