. 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.
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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
Here is the tree diagram for the given scenario:
```
C V
/ \ / \
E U E U
/|\ | /|\ |
C V C C C V C V
```
Starting from the top, the first branch represents the first spin and the second branch represents the second spin. The letters C and V represent consonants and vowels, respectively.
From the diagram, we can see that there are four possible outcomes for the two spins that have a consonant on the first spin and a vowel on the second spin: EC, UC, VC, and EV. So, the probability of this occurring is:
P(consonant first, vowel second) = P(EC) + P(UC) + P(VC) + P(EV)
P(EC) = 1/3 * 2/3 = 2/9 (probability of landing on a consonant on the first spin is 2/3, and on the second spin is 1/3)
P(UC) = 1/3 * 1/3 = 1/9 (probability of landing on a vowel on the first spin is 1/3, and on the second spin is 1/3)
P(VC) = 1/3 * 1/3 = 1/9 (probability of landing on a vowel on the first spin is 1/3, and on the second spin is 1/3)
P(EV) = 1/3 * 1/3 = 1/9 (probability of landing on a consonant on the first spin is 2/3, and on the second spin is 1/3)
Therefore,
P(consonant first, vowel second) = 2/9 + 1/9 + 1/9 + 1/9 = 5/9
Thus, the probability that the spinner will land on a consonant the first time and a vowel the second time is 5/9.
To find the probability of landing on a consonant the first time and a vowel the second time when spinning a spinner twice, we can create a tree diagram of all possible outcomes.
Step 1: Determine the possible outcomes for the first spin. Since the spinner is divided into equal parts, let's assume there are 4 possible outcomes: C1, C2, V1, and V2, where C represents a consonant and V represents a vowel.
C1
/ \
/ \
C2 V1
/
/
V2
Step 2: Determine the possible outcomes for the second spin. Since the first outcome C1 leads to C2 and V1, C2 leads to V2, and V1 leads to C2, our tree diagram expands as follows:
C1
/ \
/ \
C2 V1
/ \ / \
/ \ / \
V2 V2 C2 C2
Step 3: Assign probabilities to each outcome. Let's assume that each outcome has an equal probability of occurring, meaning each branch has a 1/4 probability.
C1
/ \
1/4 1/4
/ \
/ \
V2 V2
1/4 1/4
C1
/ \
1/4 1/4
/ \
/ \
C2 V1
1/4 1/4
Step 4: Determine the desired outcome. We want to find the probability of landing on a consonant the first time and a vowel the second time. Looking at the tree diagram, we can see that there are two outcomes that match this description: C1 -> V2 and C1 -> V1.
Step 5: Calculate the probability. The probability of C1 -> V2 is 1/4 * 1/4 = 1/16, and the probability of C1 -> V1 is 1/4 * 1/4 = 1/16. Since these two outcomes are mutually exclusive (they cannot occur at the same time), we can add their probabilities together:
1/16 + 1/16 = 2/16 = 1/8
Therefore, the probability that the spinner will land on a consonant the first time and a vowel the second time is 1/8.