TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Levajkovic)/Übungen 2023W/HW01.2

Passwords

Anna needs to choose a password for her computer account, that is a sequence of eight characters consisting of uppercase letters, lowercase letters and digits. The rule is that the password must consist of two lowercase letters (a to z) followed by one uppercase letter (A to Z) followed by five digits $(0,1,\dots ,9)$. For example, mhT26039 is a valid password. A hacker has been able to write a program that randomly and independently generates 107 passwords according to the above rule. Note that the same password could be generated more than once. If one of the randomly chosen passwords matches Anna’s password, then the hacker can access her account information. What is the probability that the hacker is successful in accessing her account

information?

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Lösungsvorschlag von Lessi

--Lessi 2024-02-07T13:04:11Z

1) How many passwords are possible at all? We use combination with repetitions and order.

possible <- 26^3 * 10^5
possible

2) Now the probability that one password is in the hackers list is:

(10^7 / possible) * 100

Probability is at most 0.57% (if every generated password is unique)