Maria''s phone has a 4-digit passcode, each digit is chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

Question

The phone is designed to allow a passcode to be entered once every 5 seconds. Unfortunately, Maria has lost her memory. To get into the phone, she has to guess the passcode, but she cannot remember the previous codes that she guessed (so, her guesses are independent). If Maria enters a passcode every 5 seconds, what is the expected time it will take Maria to guess her passcode? Give your answer in hours.

Answer 1

Well there are 10 x 10 x 10 x 10 possibilities (4 digits, each with 10 possibilities)

So it takes 10 x 10 x 10 x 10 x 5 seconds

3600 seconds in 1 hr

so (10 x 10 x 10 x 10 x 5 ) / 3600 hours