I got a problem with a question.
The question is as follows:
There is a person that needs to open 3 locks. In total got he got 11 keys, but he forgot what key belongs to what lock, so he is going to try all the keys, but the problem is everytime he tries a key he forget that he used that key. So it could be possible that the first locks he opens with 100 tries, the second lock with 4 keys and the third with only 1 key.
I need to answer the following question:
Show that X is the total times keys he tries. What is P(X=k) in k∈N? What is the expected value?
My problem with this question is that I’m sure how to do this, because I can’t calculate the answer, because I do not now how many time he is going to try. For now I got the following answer:
But I’m not sure if that’s correct. Could anybody tell me if this is correct? If you need to know of how I got to this answer, please ask.