Counting A computer hacker is trying to break into a computer system by guessing
ID: 3047761 • Letter: C
Question
Counting A computer hacker is trying to break into a computer system by guessing the system administrator's password. The hacker can try 15 passwords a minute, but if he tries unsuccessfully for more than 12 minutes a day, he will get caught. If he limits his attempts to at most 12 minutes each day, he will not get caught. The hacker knows that the administrator's password is at least 6 and at most 10 characters long, does not contain any character that is not a number, an uppercase letter, or a lowercase letter (no special characters such as spaces, punctuation marks, dollar signs, etc.), and that the first character is a letter. Case matters, and characters can be repeated. Problem 11 What fraction of the passwords that start with a letter, contain only numbers and upper and lowercase letters, and are at least 6 and at most 10 characters long can the hacker try in 9 years without getting caught? (Assume that every year lasts 365.25 days.) (Q11)Explanation / Answer
for 9 year number of attemts =15*12*365.25*9=591705
as for each charecter we have 62 possibilities except first for which 52 possibilities (26 lower; 26upper aplpha and 10 digits)
possible passwords=N(6 letter +7 letter +8 letter +9 leter +10 letter) passwords
=52*(625+626+627+628+629) =7.15468*1017
probability of hacking 591705/7.15468*1017 =8.27018*10-13