Basic Concepts of Probability and Counting
1. License plates are made using 3 letters followed by 2 digits. How many different plates can be made if repetition of letters and digits is allowed?
(26^3)(10^2) = (17576)(100) = 1,757,600
yes
a password consists of two letters followed by a five-digit number. how many passwords are possible if (a)there are no restriction and (b)none of the letters or digits can be repeated? what is the probability of guessing the password in one if there no restriction?
does anyone have the answers to the lesson 1 basic concepts of probability quiz for unit 9
To answer this question, we need to understand the concept of counting and multiplication principle in probability.
In this scenario, we are making license plates using 3 letters and 2 digits. Let's break it down step by step:
1. Counting the number of possibilities for each element:
- There are 26 letters in the English alphabet (from A to Z).
- There are 10 digits (from 0 to 9).
2. For the first letter, we have 26 choices. Similarly, for the second and third letters, we also have 26 choices each. So the total number of possibilities for the letters is 26 * 26 * 26 = 26^3.
3. For the first digit, we have 10 choices. Similarly, for the second digit, we also have 10 choices. So the total number of possibilities for the digits is 10 * 10 = 10^2.
4. Finally, to find the total number of different license plates that can be made, we multiply the number of possibilities for the letters (26^3) by the number of possibilities for the digits (10^2). This gives us (26^3)(10^2) = (17576)(100) = 1,757,600.
Therefore, there are 1,757,600 different license plates that can be made if repetition of letters and digits is allowed.