To find the probability that the car has the two letters together, we need to determine the total number of possible license plates and the number of license plates that have the two letters together.
Let's break down the problem:
1. Total number of license plates:
Since the plate consists of two letters and four digits, we have a total of 26 letters in the English alphabet (excluding I and O) and 10 digits (0-9). The first letter can be any letter from A to Z (excluding I and O), and the second letter can also be any letter from A to Z (excluding I and O). Therefore, the total number of choices for the two letters is 24 * 24 = 576. The four digits can be any of the ten digits, so the total number of choices for the digits is 10,000. Therefore, the total number of possible license plates is 576 * 10,000 = 5,760,000.
2. Number of license plates with the two letters together:
To calculate the number of license plates with the two letters together, we can treat the two letters as a single entity. So effectively, we have 25 options (A to Z excluding I and O) for the combined letters, and the digits remain the same, giving us 10,000 choices. Therefore, the number of license plates with the two letters together is 25 * 10,000 = 250,000.
Now that we have the total number of choices and the number of choices with the two letters together, we can calculate the probability:
Probability = (Number of choices with the two letters together) / (Total number of choices)
Probability = 250,000 / 5,760,000
Simplifying the fraction, we get:
Probability = 25/576
So, the probability that the car has the two letters together on the license plate is 25/576.