Well, when it comes to license plates, it can feel like you're playing a game of "Wheel of Fortune." So let's spin that imaginary wheel and see what we get! In this case, we're looking for a repeated letter or digit.
To calculate the probability, we need to figure out how many options we have for each segment.
For the first segment of four letters, we have 26 options (A-Z) for each letter. So that's 26^4.
For the second segment of two numerals, we have 10 options (0-9) for each number. So that's 10^2.
Lastly, for the final two letter segment, we also have 26 options (A-Z) for each letter. So that's 26^2.
Now, to determine the number of license plates with repeated letters or digits, we need to subtract the number of license plates with no repeated letters or digits from the total number of possible license plates.
The formula becomes: (total number of possible plates) - (number of plates with no repeats).
Total number of possible plates = 26^4 * 10^2 * 26^2
Now, let's calculate the number of plates with no repeats.
For the first segment of four letters, we have 26 options (A-Z) for each letter. However, since we can't repeat any letter, after choosing the first letter we have 25 options, then 24 options for the next letter, then 23 options for the third letter, and finally 22 options for the fourth letter. So that's 26 * 25 * 24 * 23.
For the second segment of two numerals, we have 10 options (0-9) for the first number, and then 9 options for the second number (since we can't repeat). So that's 10 * 9.
Lastly, for the final two letter segment, we also have 26 options (A-Z) for the first letter, and then 25 options for the second letter (since we can't repeat). So that's 26 * 25.
Now, let's calculate the number of license plates with no repeats: 26 * 25 * 24 * 23 * 10 * 9 * 26 * 25.
To find the number of license plates with repeated letters or digits, we subtract the number of plates with no repeats from the total number of possible plates:
(26^4 * 10^2 * 26^2) - (26 * 25 * 24 * 23 * 10 * 9 * 26 * 25).
Now, let's divide the number of plates with repeated letters or digits by the total number of possible plates, and multiply by 100 to get a percentage.
And voila! The probability of getting a license plate with a repeated letter or digit is the result of that calculation, rounded to the nearest whole percent. I'll let you plug in the numbers and do the math. Good luck!