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 6. Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on her first try? Round to six decimal places. Probability =
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 6. Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on her first try? Round to six decimal places. Probability =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Probability of Guessing a Password on the First Try
**Scenario:**
A hacker is attempting to guess someone's password. The hacker knows that:
1. The password is 5 digits long.
2. Each digit can be a number between 0 and 6 (inclusive).
Given that the hacker makes random guesses, what is the probability that the hacker guesses the password correctly on the first attempt? Round your answer to six decimal places.
**Question:**
What is the probability that the hacker guesses the password on the first try?
**Answer:**
\[ \text{Probability} = \_\_\_\_\_\_ \]
### Explanation:
The task here is to find the exact probability that a randomly guessed password will match the correct 5-digit password. Each position in the 5-digit number can be any digit from 0 to 6, providing a total of \(7^5\) possible combinations. The probability of guessing the one correct combination out of all possible combinations can be calculated as follows:
\[ \text{Probability} = \frac{1}{7^5} \]
By calculating the value and rounding it to six decimal places, you can find the exact probability of the hacker guessing the password correctly on the first try.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f8e4cad-17a8-4afc-8111-d96bcef8136e%2Fc8fffc5f-967d-47a5-9e7c-1e3158f9af0c%2Fyd9t9sr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability of Guessing a Password on the First Try
**Scenario:**
A hacker is attempting to guess someone's password. The hacker knows that:
1. The password is 5 digits long.
2. Each digit can be a number between 0 and 6 (inclusive).
Given that the hacker makes random guesses, what is the probability that the hacker guesses the password correctly on the first attempt? Round your answer to six decimal places.
**Question:**
What is the probability that the hacker guesses the password on the first try?
**Answer:**
\[ \text{Probability} = \_\_\_\_\_\_ \]
### Explanation:
The task here is to find the exact probability that a randomly guessed password will match the correct 5-digit password. Each position in the 5-digit number can be any digit from 0 to 6, providing a total of \(7^5\) possible combinations. The probability of guessing the one correct combination out of all possible combinations can be calculated as follows:
\[ \text{Probability} = \frac{1}{7^5} \]
By calculating the value and rounding it to six decimal places, you can find the exact probability of the hacker guessing the password correctly on the first try.
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