Part 1: Consonants and Vowels
The sections on the spinner are as follows: A, B, C, D, E, F, G, H.
Vowels:
- A
- E
Consonants:
- B
- C
- D
- F
- G
- H
There are:
- Consonants: 6 (B, C, D, F, G, H)
- Vowels: 2 (A, E)
Part 2: Theoretical Probability of Landing on a Consonant
The theoretical probability is calculated by dividing the number of favorable outcomes by the total number of outcomes.
- Number of consonants: 6
- Total sections on the spinner: 8
The probability \( P \) that the spinner will land on a consonant is:
\[ P(\text{consonant}) = \frac{\text{Number of consonants}}{\text{Total sections}} = \frac{6}{8} \]
To simplify this fraction, divide the numerator and the denominator by 2:
\[ P(\text{consonant}) = \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \]
Part 3: Expected Times the Spinner Lands on a Consonant
If the spinner is used 160 times, we can calculate the expected number of times it will land on a consonant by multiplying the total spins by the probability of landing on a consonant:
\[ \text{Expected times} = \text{Total spins} \times P(\text{consonant}) = 160 \times \frac{3}{4} \]
Calculating this gives:
\[ \text{Expected times} = 160 \times 0.75 = 120 \]
The spinner is expected to land on a consonant 120 times.
Summary of Answers:
- Consonants: 6
- Vowels: 2
- Theoretical Probability of a Consonant: \(\frac{3}{4}\)
- Expected Times Landing on a Consonant: 120 times.