SOLUTION: Hello Guys, I think I got it can you please check it for me here is the question and the answer. A mini license plate for a toy car must consist of a letter followed by two n

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Question 269551: Hello Guys,
I think I got it can you please check it for me here is the question and the answer.
A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be an R, U or N. Each number must be a 2 or 6. Repetition of digits is permitted.
Thank you,
1.Use the counting principle to determine the number of points in the sample space.

2.Construct a tree diagram to represent this situation and submit it to the week 5, assignment 3 dropbox.

3.List the sample space.

4.Determine the exact probability of creating a mini license plate with an R. Give solution exactly in reduced fraction form.

HERE IS MY ANSWER:
First our license plate must be in the form of
# - L - L,
or,
number - letter - letter.
we have 2 choices for the numbers, 2 or 6
we have 3 choices for the letters r - u - n.
repetition is allowed: So there is a second 3 choices for letters r - u - n
---
1. Use the counting principle to determine the number of points in the sample space.
ANSWER: The counting principal is all about multiplying the number of ways one event occurs x the number of ways a second event occurs x the number of ways a third event occurs and so on. In our case we have 2 number choices and 3 letter choices, but two times.
2 x 3 x 3 = 18.
---
2. Construct a tree diagram to represent this situation.
ANSWER:
step 1 - write a 2 and below it with a little space write a 6
step 2 - from the 2 draw 3 arrows and next to the end of these write R,U, N
step 3 - next to each of the letters draw another 3 arrows and write the letters again for R,U,N
step 4 - from the 6 draw 3 arrows and next to the end of these write R,U,N
step 5 - next to each of the letters draw another 3 arrows and write the letters again for R,U,N
---
3. List the sample space.
ANSWER: this is pretty straight forward from the tree diagram. we get
2aa, 2ab, 2ac, 2ba, 2bb, 2bc, 2ca, 2cb, 2cc,
6aa, 6ab, 6ac, 6ba, 6bb, 6bc, 6ca, 6cb, 6cc.
2ab plate is different from 2ba plate
---
4. Determine the EXACT probability of creating a mini license plate with a R. Give the solution in reduced fraction form.
ANSWER: 2ac, 2bc, 2cc, 2ca, 2cb, 6ac, 6bc, 6cc, 6ca, 6cb
"with a R" means to me one or two R"s in any order.
P(R) = 10/18 = 5/9.
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
Here are my answers.  They don't agree with yours.  


A mini license plate for a toy car must consist of a letter followed by two
numbers. Each letter must be an R, U or N. Each number must be a 2 or 6.
Repetition of digits is permitted. 

1.Use the counting principle to determine the number of points in the sample
space. 

Here's a sample license plate:   U66

Choose a letter to go where the U is -- 3 ways
Choose a digit to go where the first 6 is -- 2 ways
Choose a digit to go where the second 6 is -- 2 ways.

That's 3*2*2 = 12 


 
2.Construct a tree diagram to represent this situation and submit it to the
week 5, assignment 3 dropbox. 

                               2
                            2 
                          /    6
                        R    
                      /   \    2
                    /       6    
                  /            6
                /               
              /                2
            /               2
          /               /    6
        /-  - - - - - - -U     
         \                 \   2
           \                 6
             \                 6
               \
                 \             2
                   \        2
                      \    /   6
                        N
                          \    2
                           6
                               6 



3.List the sample space. 

{R22, R26, R62, R66, U22, U26, U62, U66, N22, N26, N62, N66}.

4.Determine the exact probability of creating a mini license plate with an R.
Give solution exactly in reduced fraction form.

The first 4 have R's.  That's 4 out of the 12, so the probability is 



Edwin
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