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The local YMCA has new locker rooms with built-in 3-digit combination locks. If I understand the Birthday Paradox correctly, I have a better than 50% chance of finding a lock combination with 33 tries on a given lock. (The lock combination gets set by the member at the time of locking the locker door.)

Is my analysis correct?

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No, that is not correct. Assuming that the lock combinations are assigned randomly, and you have no apriori knowledge of the combination, you need 500 tries before you get a 50% chance of success.

What the birthday paradox means is that if you have 38 locks (not 33, and assuming that the combinations were assigned randomly and independently), there is a better than 50% chance there are two locks with the same combination. This doesn't help you with finding the combination of any particular lock.

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  • $\begingroup$ That leaves me feeling much better about locker-contents security! +1 for clear explanation of my misunderstanding. $\endgroup$ Feb 7 '17 at 23:24

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