Question

A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 15 characters long, and that each character is either lowercase, an uppercase letter or a numerical digit. Assume that the hacker makes a random guess.

What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction.

Answer 1

The probability that the hacker guesses the password correctly on the first try is 1 / 62^15.

Step-by-step explanation:

To calculate the probability that the hacker guesses the password correctly on the first try, we need to determine the total number of possible passwords and divide it by the total number of possible guesses.

Since the password is 15 characters long and each character can be a lowercase letter, an uppercase letter, or a numerical digit, there are 26 + 26 + 10 = 62 possible options for each character.

Therefore, the total number of possible passwords is 62^15 (62 raised to the power of 15).

The probability of the hacker guessing the password correctly on the first try is 1 divided by the total number of possible passwords.

So, the probability is 1 / 62^15. This can be left as a fraction or converted to a decimal.

Answer 2

There are 26 possible lowercase letters, 26 possible uppercase letters, and 10 possible numbers (0-9). 26+26+10=62 That means there's a 1/62 chance that they get one letter right. But there's 15 letters. They're chance would decrease each time to get it exact. 1/62 divided by 15/1 = 1/832 So there is a 1 in 832 chance that the hacker guesses it correct first try with that information.