Question
A 6 sided spinner has sides labelled A, B, C, D, E, F. In 120 spins, how many times can you expect to land on a vowel?
Answers
GPT-4o mini
To determine the expected number of times the spinner will land on a vowel in 120 spins, we first need to identify the vowels on the spinner. The labels on the sides of the spinner are A, B, C, D, E, and F.
The vowels in this case are A and E. Thus, there are 2 vowels out of the 6 sides:
- Vowels: A, E
- Consonants: B, C, D, F
The probability of landing on a vowel in a single spin is given by:
\[
P(\text{vowel}) = \frac{\text{Number of vowels}}{\text{Total sides}} = \frac{2}{6} = \frac{1}{3}
\]
Now, if we spin the spinner 120 times, the expected number of times it will land on a vowel can be calculated by multiplying the probability of landing on a vowel by the total number of spins:
\[
\text{Expected number of vowels} = P(\text{vowel}) \times \text{Total spins} = \frac{1}{3} \times 120
\]
Calculating this gives:
\[
\text{Expected number of vowels} = \frac{120}{3} = 40
\]
Therefore, in 120 spins, we can expect the spinner to land on a vowel **40 times**.
The vowels in this case are A and E. Thus, there are 2 vowels out of the 6 sides:
- Vowels: A, E
- Consonants: B, C, D, F
The probability of landing on a vowel in a single spin is given by:
\[
P(\text{vowel}) = \frac{\text{Number of vowels}}{\text{Total sides}} = \frac{2}{6} = \frac{1}{3}
\]
Now, if we spin the spinner 120 times, the expected number of times it will land on a vowel can be calculated by multiplying the probability of landing on a vowel by the total number of spins:
\[
\text{Expected number of vowels} = P(\text{vowel}) \times \text{Total spins} = \frac{1}{3} \times 120
\]
Calculating this gives:
\[
\text{Expected number of vowels} = \frac{120}{3} = 40
\]
Therefore, in 120 spins, we can expect the spinner to land on a vowel **40 times**.