The spinner is divided into equal parts. Use a tree diagram to find the probability that the spinner will land on a consonant the first time and a vowel the second time if the spinner is spun twice.
A circle is divided equally into three sections.· One of the sections is labeled with an upper E.
· One of the sections is labeled with an upper U.
· One of the sections is labeled with an upper N.
· An arrow originating from the center of the circle is pointing at the section labeled with upper U. (1 point)
two-thirds
two-ninths
three-fourths
start fraction 5 over 9 end fraction
Using a tree diagram, we can easily see the possible outcomes of spinning the spinner twice:
C V
/ \ / \
C V C V
/ \ / \ / \ / \
C V C V C V C V
There are a total of 4 outcomes where the spinner lands on a consonant the first time and a vowel the second time (shown in bold).
Therefore, the probability of this happening is 4/8 or 1/2.
Regarding the second problem, since only one section is labeled with an upper U out of three total sections, the probability of the arrow pointing at the U section is 1/3. Thus, the answer is:
start fraction 1 over 3 end fraction
To find the probability of the spinner landing on a consonant the first time and a vowel the second time, we can use a tree diagram.
First, let's list all the possible outcomes for the first spin:
- Consonant (C)
- Vowel (V)
Next, for each outcome of the first spin, list all the possible outcomes for the second spin:
- If the first spin is a consonant (C), the possible outcomes for the second spin are:
- Consonant (CC)
- Vowel (CV)
- If the first spin is a vowel (V), the possible outcomes for the second spin are:
- Consonant (VC)
- Vowel (VV)
Now, draw a tree diagram to visualize the outcomes:
C V
/ \ / \
CC CV VC VV
Now, we can see there are 2 outcomes where the spinner lands on a consonant the first time and a vowel the second time: CV and VC.
Since there are a total of 4 possible outcomes (CC, CV, VC, VV), the probability of the spinner landing on a consonant the first time and a vowel the second time is 2 out of 4, which simplifies to 1/2.
So, the correct answer is: one-half.