Quincy’s password to his online account is allowed to contain letters or digits. Quincy uses his dog’s name, Buddy, as his password. The password is not case sensitive, meaning that Buddy, buddy, and buDDy are equivalent. Quincy lets his friend know that his password is exactly 5 characters long and is made up of letters only. What is the probability that Quincy’s friend can guess his password in one try? Show your work.

Quincy’s bank changes its webpage so that passwords are case-sensitive. This means that Buddy, buddy, and buDDy are now considered three different passwords. Quincy tells his friend, “This makes it twice as unlikely for you to guess my password.” Is Quincy’s statement correct? Explain.

Quincy’s friend has a program that can test 100,000 passwords per second. Given what Quincy’s friend knows about Quincy’s password, how long would it take him to test all the possibilities? How much longer would it take Quincy’s friend to test all the possible passwords if he knew that Quincy’s password was 5 characters long, but did not know whether those characters were letters or digits? Show your work.