Question

A spinner has 8 equally sized sections labeled as A, B, C, D, E, F, G, H.(4 points)
Part 1: How many consonants and vowels are listed on the spinner?

consonants

vowels

Part 2: What is the theoretical probability the spinner will land on a consonant?

Enter the probability as a simplified fraction.

Part 3: If the the spinner is used 160 times, how many times should the spinner land on a consonant?

The spinner is expected to land on a consonant
times.

Answer 1

**Part 1: How many consonants and vowels are listed on the spinner?**

From the labels on the spinner (A, B, C, D, E, F, G, H):
- Vowels: A, E (2 vowels)
- Consonants: B, C, D, F, G, H (6 consonants)

So, we have:
- **Consonants:** 6
- **Vowels:** 2

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**Part 2: What is the theoretical probability the spinner will land on a consonant?**

The total number of sections on the spinner is 8. The number of consonant sections is 6.

The probability of landing on a consonant can be calculated using the formula:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{8}
\]

Now, simplifying the fraction:

\[
\frac{6}{8} = \frac{3}{4}
\]

So, the theoretical probability the spinner will land on a consonant is:

**Probability = \(\frac{3}{4}\)**

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**Part 3: If the spinner is used 160 times, how many times should the spinner land on a consonant?**

To find the expected number of times the spinner will land on a consonant out of 160 spins, we can multiply the total number of spins by the probability of landing on a consonant:

\[
\text{Expected number of consonants} = \text{Total spins} \times \text{Probability of consonant} = 160 \times \frac{3}{4}
\]

Calculating this gives:

\[
160 \times \frac{3}{4} = 160 \times 0.75 = 120
\]

Thus, the spinner is expected to land on a consonant **120 times**.