A janitor owns a keychain with 5 identical looking keys on the chain. His must open a particular office door, but he can’t remember which key opens the door. He decides to try the keys randomly, in such a way that if a key doesn’t work he eliminates it as a candidate. What is the chance that he opens the door on the second attempt? What is the expected number of attempts needed to open the door? At the next office, he has the same problem.. but this time he is too lazy to eliminate the keys that didn’t work. Instead, he just tries keys one after the other until he gets in. Is this approach expected to take more tries? Explain your answer.

A janitor owns a keychain with 5 identical looking keys on the chain. His must open a particular office door, but he can’t remember which key opens the door. He decides to try the keys randomly, in such a way that if a key doesn’t work he eliminates it as a candidate. What is the chance that he opens the door on the second attempt? What is the expected number of attempts needed to open the door? At the next office, he has the same problem.. but this time he is too lazy to eliminate the keys that didn’t work. Instead, he just tries keys one after the other until he gets in. Is this approach expected to take more tries? Explain your answer.