To solve the problems related to the spinner, let's break it down into parts.
Part 1: Contestants and Vowels
The spinner has the sections labeled A, B, C, D, E, F, G, H.
- Vowels: A, E (there are 2 vowels)
- Consonants: B, C, D, F, G, H (there are 6 consonants)
So, the spinner has:
- Number of contestants (sections): 8
- Number of vowels: 2
Part 2: Theoretical Probability of Landing on a Consonant
To find the probability of landing on a consonant:
- Total sections = 8
- Number of consonants = 6
The probability \( P \) of landing on a consonant is calculated as: \[ P(\text{consonant}) = \frac{\text{Number of consonants}}{\text{Total sections}} = \frac{6}{8} = \frac{3}{4} \]
Part 3: Expected Number of Times Landing on a Consonant
If the spinner is used 160 times, the expected number of times it will land on a consonant can be calculated by multiplying the total spins by the probability of landing on a consonant.
So: \[ \text{Expected number of times} = 160 \times P(\text{consonant}) = 160 \times \frac{3}{4} = 160 \times 0.75 = 120 \]
Summary of Answers
- Part 1: 8 contestants and 2 vowels.
- Part 2: The theoretical probability the spinner will land on a consonant is \( \frac{3}{4} \).
- Part 3: The spinner is expected to land on a consonant 120 times.