Question

A hacker is trying to guess someone's password. the hacker knows (somehow) that the password is 12 characters long, and that each character is either a lowercase letter, (a, b, c, etc), an uppercase letter (a, b, c, etc) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). assume that the hacker makes random guesses.

Answer 1

Determine first the places that will be filled:

26 + 26 + 10 = 62 ways

The number of possible passwords is limited to 12 characters
Thus,

= 62^12 (assume that repetition is allowed)

The probability of guessing correctly = 

(1/62)^12
= 3.099557704 x 10^-22 (note that it is in scientific notation form)