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?
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.
