# Tree Diagrams

#### aburchett

##### New member
A mini license plate for a toy car must consist of a two numbers followed by a vowel. Each number must be a 3 or a 6. 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 3. Give solution exactly in reduced fraction form.

Can you tell me if my work is correct? :

vowel= a, e, i, o, u = 5 vowels
numbers need to be either 3 or 6

2*1*5=10 points in the sample space

Sample Space is
36a
36e
36i
36o
36u
63a
63e
63i
63o
63u

The probabiliy of creating a mini license play with a 3 is 10/10 or 1.

#### Loren

##### Senior Member
You say numbers can be repeated, so how about 33a, etc?

Sometimes I like to analyze this way.

There are three spaces to be filled.
__ __ __

In how many ways can the first space be filled? Ans. With a 3 or a 6 --- that's 2 ways.
In how many ways can the second space be filled? Ans. With a 3 or a 6 --- that's 2 more ways.
In how many ways can the third space be filled? Ans. With any vowel (a, e, i, o, u) --- that's 5 ways.

Total ways is product --- 2 x 2 x 5 = 20.

#### Loren

##### Senior Member
Sample Space is
36a
36e
36i
36o
36u
63a
63e
63i
63o
63u

The probabiliy of creating a mini license play with a 3 is 10/10 or 1.

Your sample space is not correct. But, using it to help you understand, suppose the question said "What is the probability of creating a plate with an "e" in it. You count the number of plates that contain an "e". We see there are only 2. We use that as the numerator and the total size of the sample space is the denominator. So, the probability of a plate containing an "e" is 2/10 or 1/5.

#### aburchett

##### New member
ok so sample space is 2*2*5=20

Sample space is
36a
36e
36i
36o
36u
63a
63e
63i
63o
63u
33a
33e
33i
33o
33u
66a
66e
66i
66o
66u

and the probability of creating a mini plate with a 3 is 15/20 or 3/4.

How would I create a tree diagram for this?

#### aburchett

##### New member
nevermind, I got it.

Thanks