Question

A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 13 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.
What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.

Answer 1

There are 26 lowercase and 26 capital letters as well as 10 numerical digits, which makes for 62 total possible characters per spot. Since each of the 13 spots can be any of these 62 digits, the total number of possibilities will be 62^13. Because the hacker has to guess on the first try, he cannot rule out any possibilities. The probability that he will guess the password on the first try is 1/(62^13).