A and B are sequences of random numbers where each number is an independantly random number from 1 to 365.
i and j are sequence positions in a and b
What's the probability that the set A(1..i) intersect B(1..j) is not empty?
Update: To help frame this as a real world problem, let's say you had a company of 50 people and made the entry code to the building everyone's birthday - then someone found out this was the case - how many guesses would it statistically take to gain entry?
Note: I'm not planning a heist.