suppose a license plate for a car has 4 letters followed by 1 number and 3 more letters. The letters and numbers are chosen randomly.

a. how many license plates are possible?

b. compare the probability that a license plate spells math4you with the probability that the first 4 letters spell math.

Each letter has a probability of 1/26 and the numeral has a 1/10 probability. Multiply the eight probabilities and the denominator of the product will be you answer for a.

The probability for "math4you" is the above product. The probability for "math" = (1/26)^4.

I hope this helps. Thanks for asking.

To find the number of possible license plates, we need to consider the number of choices for each position.

a.

1. For the first letter, we have 26 options (any letter of the alphabet).
2. Similarly, for the second, third, and fourth letters, we also have 26 options each.
3. For the number in the fifth position, we have 10 options (0 to 9).
4. Finally, for the sixth, seventh, and eighth letters, we again have 26 options each.

Therefore, the total number of possible license plates is calculated as:

26 * 26 * 26 * 26 * 10 * 26 * 26 * 26 = 17,576,000

So, there are 17,576,000 possible license plates.

b.

Now, let's compare the probability of the license plate "math4you" to the probability of the first four letters spelling "math."

To calculate the probability, we need to divide the number of favorable outcomes by the total number of possible outcomes.

1. For the license plate "math4you":
- The first letter "m" has a probability of 1/26.
- The second, third, and fourth letters are fixed as "a," "t," and "h."
- The number "4" has a probability of 1/10.
- The fifth letter "y" has a probability of 1/26.
- The sixth, seventh, and eighth letters are fixed as "o," "u," and "r."

Therefore, the probability of getting the license plate "math4you" is:
(1/26) * 1 * 1 * 1 * (1/10) * (1/26) * 1 * 1 * 1 = 1/(26*10*26) = 1/6760.

2. For the license plate "math":
- The first letter "m" has a probability of 1/26.
- The second, third, and fourth letters are fixed as "a," "t," and "h."

Therefore, the probability of getting the license plate "math" is:
(1/26) * 1 * 1 * 1 = 1/26.

Comparing the two probabilities, we find that:
1/6760 is less likely to occur than 1/26.

Hence, the probability of getting the license plate "math4you" is lower than the probability of the first four letters spelling "math."