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.

Question

A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 14 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

First figure out how many possible passwords there are:

Since each character can either be a lower case or upper case letter (52 possibilities) or a digit from 0 to 9 (10) possibilities, each character has 62 possible values. Since each of the 14 characters can be any of these possible values, there are 62^14 possible arrangements of the password.

There is only one possible arrangement of the password that is valid, so the probability that the hacker guesses the password on the first try is 1 out of 62^14.