Question

A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 5 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? Round to six decimal places.

A. 0.000000
B. 0.000625
C. 0.001250
D. 0.001563

Answer 1

The probability of guessing a 5-digit password (digits 0-5) on the first try is 1 in 6^5, or 0.0001286 when rounded to six decimal places, which is closest to 0.000129 and does not match the provided options.

Step-by-step explanation:

The probability of the hacker guessing a 5-digit password correctly on the first try, with each digit ranging from 0 to 5, is calculated by considering the total number of possible combinations. Since there are 6 choices (0-5) for each of the 5 digits, there are 6^5 or 7776 different possible combinations. Thus, the probability of guessing the password on the first attempt is 1 divided by the total number of combinations, which gives us a probability of 0.0001286, rounded to six decimal places.

However, rounding this number to six decimal places as per the options provided in the question, the closest answer is 0.000129. None of the provided options (A, B, C, D) in the question exactly match this result, perhaps indicating a typo or a miscalculation in the question itself.