In Exercises 49-53, use counting principles to find the probab...

Question

In Exercises 49-53, use counting principles to find the probability.

50. A security code consists of three letters and one digit. The first letter cannot be A, B, or C. What is the probability of guessing the security code on the first try?

Accepted Answer

Hello everyone. Let's take a look at this question together. A locker code consists of three colors followed by one digit. The available colors are red, green, blue, yellow, orange, purple, white, black, gray, and pink. However, the first color cannot be red, green, or blue. The digits range from 0 to 9. If colors and digits can repeat, what is the probability of randomly guessing the correct code on the first draw? Is it answer choice A, 1 out of 7000, answer choice B, 1 out of 5000, answer choice C, 1 out of 10,000, or answer choice D 1 out of 6000? So in order to solve this question, we have to determine the probability of randomly guessing the correct code for the locker on the first try when we know the code consists of three colors, followed by 1 digit, and we have our available colors. And our digits range from 0 to 9, as well as the first color cannot be red, green, or blue, and the colors and digits can repeat. And the first step in determining this probability is to identify the total options for each part of the code. Where we know that there are 10 colors in total and the first color cannot be red, green, or blue, and the 2nd and 3rd colors have no restrictions, as well as the digit can be any one of 10 digits as they are from 0 to 9. So then we can count the total codes or the arrangements. As we know, each part of the code is chosen independently, and the order matters, so we count the number of possible arrangements as the following where the total number of possible codes is equal to 7 multiplied by 10, multiplied by 10, multiplied by 10, which is equal to 7000. And then we can calculate the probability. And since only one code is correct, the probability of guessing it on the first try is 1 out of 7000, as there are 7000 total possible arrangements for the locker code. And looking at our answer choices, we can identify that answer choice A is the correct answer, as answer choice A is 1 out of 7000, which is the probability of guessing the locker code on the first draw, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

In Exercises 49-53, use counting principles to find the probability.
50. A security code consists of three letters and one digit. The first letter cannot be A, B, or C. What is the probability of guessing the security code on the first try?

Key Concepts

Counting Principles

Probability

Permutations and Combinations

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