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

8.063 × 10²⁶

Explanation:

From the given information:

Since the hacker knows that the character are lowercases letter, uppercases letter or numerical digits from (0-9).

Then, we have the total number of characters to be:

= 26 + 26 + 10

= 62

Now, for each of the 14 places, we can fill it up with 62 possible ways.

Thus, the probability that the hacker guesses in his first trial is:

`=( (1)/(62))^{14`

`=( 0.016129)^{14`

= 8.063 × 10²⁶