SOLUTION: A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 4 digits long, and that each digit could be a number between 0 and 5. Assume that th
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Question 1200499: A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 4 digits long, and that each digit could be a number between 0 and 5. Assume that the hacker makes random guesses.
What is the probability that the hacker guesses the password on his first try? Please report the answer to four decimal places.
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A hacker is trying to guess someone's password. The hacker knows (somehow)
that the password is 4 digits long, and that each digit could be a number
between 0 and 5. Assume that the hacker makes random guesses.
What is the probability that the hacker guesses the password on his first try?
Please report the answer to four decimal places.
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There are 4 positions in the password, and there are 6 independent possibilities
in each position (the digits from 0 to 5 inclusive).
So, = 1296 different passwords are possible; of them, only one is correct.
Thus the probability to guess the right password at first attempt is
= 0.0007716 (rounded). ANSWER
A = 1 = number of correct passwords
B = 6*6*6*6 = 6^4 = 1296 = number of possible 4-digit passwords such that each digit is between 0 and 5 (there are 5-0+1 = 6 choices per digit)
Repeated digits are allowed.
A/B = 1/1296
A/B = 0.00077160493828
A/B = 0.0008 is the approximate probability they correctly guess the password on the first try if guessing at random.
This is about a 0.08% chance.
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