We have a key ring with 6 keys, but only one key opens the door. We test the keys to the door with no preference until we find the right key. Now we have two different cases:
1) At the first case when a key is not the right one we discard it and try the next one until we find the right one.
2) At the second case we have amnesia so when we try a key and its a wrong one we put it back in the key ring and we start again from the beginning to find the right key.
For both cases find the probabilities to: How many tries we will need in average, and the probability to find the right key exactly at the 4th try.