A person's building access code is their first and last initia...

Question

A person's building access code is their first and last initials and four digits.

You know a person's first name only, and you know that the last digit is odd. What is the probability of guessing this person's code on the first try?

Accepted Answer

Hello everyone. Let's take a look at this question together. A company secure login consists of the employee's department initial, the last name initial, and a three digit code. You know the department the employee works in, and you also know that the last digit of the code is even. What is the probability of correctly guessing the employee's login on the first attempt? Is it answer choice A, 1 out of 338,000? Answer choice B, 1 out of 270,400, answer choice C, 1 out of 13,000, or answer choice D, 1 out of 6500. So in order to solve this question, we need to determine the probability of correctly guessing the employee's login on the first attempt, where we know that the login consists of the employee's department initial, which we know the department the employee works in, the last name initial, and a three digit code where we also know the last digit of the code is even. And so to determine the probability, we need to identify. each part of the login, which we know that the login consists of the department initial, which is known, so there's only one possibility, the last name initial, which is unknown, so there are a total of 26 possibilities, as it could be the letter A through Z, and a 3 digit code where each digit is 0 to 9, but we know that the last digit must be even, so there are only 5. digits. And then we need to count the possibilities for each part where the department initial has only one possibility since this is known, the last name initial has 26 possibilities as it is A through Z. The first digit of code has 10 possibilities as it's a digit from 0 to 9, then the second digit of code also has 10 possibilities, since it is also a digit from 0 to 9. And lastly, the third digit of the code has 5 possibilities, since it must be an even number, so it is either 0246, or 8. And then our next step is to multiply the number of choices, which by the fundamental counting principle, the total number of outcomes is the product of the number of choices for each part, therefore, the total number. Of possible logins is calculated as 1 multiplied by 26, multiplied by 10, multiplied by 10, multiplied by 5, which is equal to 13,000. As we know that the total number of possible logins is calculated as the product of the number of choices for each part, so these are all the possibilities for each part of the code. Therefore, the probability of guessing the correct login code on the first try, which we know only one login is correct, so the probability of guessing it on the first try is the probability of the number of favorable outcomes out of the total number of outcomes. So it is 1 out of 13,000, which looking at our answer choices, we can identify is answer choice C, so answer choice C is correct. And all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

A person's building access code is their first and last initials and four digits.
You know a person's first name only, and you know that the last digit is odd. What is the probability of guessing this person's code on the first try?

Key Concepts

Probability

Combinatorics

Digits and Odd Numbers

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