The correct answer to this question is A. 1/n.
Why is 1/n the probability that he will succeed?
Each key has an equal probability of being the right one: Since the thief doesn't have any prior knowledge about the correct key, we can assume all keys have the same probability of fitting the lock.
Independent events: Each attempt with a key is independent of the previous attempts. The success or failure of one attempt doesn't affect the probability of success in the next attempt.
Probability of success in one attempt: The probability of the thief succeeding with any single key is 1/n, as there's just one correct key among n possibilities.
Therefore, regardless of the number of keys (n), the probability of the thief successfully opening the lock on any given attempt remains 1/n.