It was noticed that some cars have license plates with 3 letters followed by three numbers while other license plates have 3 numbers followed by 3 numbers if neither letters nor numbers can repeat what is the probability of getting the letter A in the first letter slot and getting the number 1 in the first number slot.
Can anyone please check my work:
P(A) = 1/24
P(1) = 1/10
P(A and 1) = (1/24)*(1/10)
To check your work, we need to determine the probability of getting the letter A in the first letter slot and the number 1 in the first number slot, given that neither letters nor numbers can repeat.
First, let's find the probability of getting the letter A in the first letter slot. Since there are 26 letters in the English alphabet and no letter can repeat, there are 26 options for the first letter. Therefore, the probability of getting the letter A in the first letter slot is 1/26, not 1/24 as you mentioned in your work.
Next, let's find the probability of getting the number 1 in the first number slot. Since there are 10 digits from 0 to 9 and no number can repeat, there are 10 options for the first number. Therefore, the probability of getting the number 1 in the first number slot is 1/10, which is correct.
To find the probability of both events occurring together, we multiply the individual probabilities:
P(A and 1) = P(A) * P(1) = (1/26) * (1/10) = 1/260
So, the correct answer is that the probability of getting the letter A in the first letter slot and the number 1 in the first number slot is 1/260, not (1/24) * (1/10) as you mentioned in your work.