Question

A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of digits is permitted.
Use the counting principle to determine the number of points in the sample space.
Construct a tree diagram to represent this situation and submit it to the W5: Assignment 2 Dropbox
List the sample space.
Determine the exact probability of creating a mini license plate with a 7. Give solution exactly in reduced fraction form.

Answer 1

There are three choices for each letter, and 2 choices for each digit, with repetition permitted.
The multiplication principle says that for a multipart event, you multiply together the number of choices for each part.
What would you get then?

Answer 2

I did it like this

Answer 3

Each number must be a 5, 7 or 9.

Each letter must be a "c", "a", or "n".

Repetition of digits is not permitted.

1. use the counting principle to determine the number of points in the sample space?
1st number: 3 ways

2nd number: 2 ways

letter: 3 ways

Number of points in the sample space: 3*2*3 = 18

2. Construct a tree diagram to represent this situation?

57a/57c/57n
59a/59c/59n
75a/75c/75n
79a/79c/79n
95a/95c/95n
97a/97c/97n
3. List the sample space
done

4 Determine the exact probability of creating a mini license plate with a given solution exactly in reduced fraction form.
Each pattern has probability 1/18 = 0556

Answer 4

is it good

Answer 5

You seem to be solving a different problem (no repetition, and three available digits). The solution is good for the new problem.