A new secretary has been given n computer passwords, only one of which will permit access to a computer file. Because the secretary has no idea which password is correct, he chooses one of the passwords at random and tries it. If the password is incorrect, he discards it and randomly selects another password from among those remaining, proceeding in this manner until he finds the correct password.
a What is the probability that he obtains the correct password on the first try?
b What is the probability that he obtains the correct password on the second try? The third try?
c A security system has been set up so that if three incorrect passwords are tried before the correct one, the computer file is locked and access to it denied. If n = 7, what is the probability that the secretary will gain access to the file?