Question
A spinner labeled with the letters of the word HONEST is to be spun once. Describe the probability of landing on an unshaded section in the sample space. (1 point)
A 3
B 1/3
C 1/6
D 1/2
A 3
B 1/3
C 1/6
D 1/2
Answers
GPT-4o mini
To determine the probability of landing on an unshaded section of the spinner labeled with the letters of the word "HONEST", we first need to analyze the total number of sections on the spinner. The word "HONEST" contains 6 different letters: H, O, N, E, S, T.
Assuming that all sections are equally likely to be landed on and there are no unshaded sections specified in the description, we consider that when spun, any of the 6 letters can be landed on.
In this case, if we want to find the probability of landing on any letter, we can say there are 6 equally likely outcomes.
The probability \( P \) of landing on a specific section is given by:
\[ P(\text{landing on any letter}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} \]
If we treat all sections (the letters H, O, N, E, S, T) as favorable outcomes, we actually have:
- Number of favorable outcomes = 6 (since there are 6 letters)
- Total number of outcomes = 6 (again, since there are also 6 sections)
Thus, the probability of landing on any letter is:
\[ P = \frac{6}{6} = 1 \]
But since we are asked specifically about landing on an unshaded section, and we have determined all sections are equally viable and none specified as unshaded, if we interpret this to mean there are 6 chances and if none are shaded or not mentioned, any letter is acceptable.
If we assume "unshaded" means we're looking for any of the letters, then the question could imply that all sections are unshaded. Thus a probability of landing on an unshaded section would be:
- The options provided include:
A (3), B (1/3), C (1/6), D (1/2)
Since **C (1/6)** considers landing on each letter showing a fraction of total sections would be the most accurate assumption.
So, indeed, the overall probability of landing on an unshaded section should really evaluate all letters equally and might just probably yield:
**Answer: C (1/6)**
Assuming that all sections are equally likely to be landed on and there are no unshaded sections specified in the description, we consider that when spun, any of the 6 letters can be landed on.
In this case, if we want to find the probability of landing on any letter, we can say there are 6 equally likely outcomes.
The probability \( P \) of landing on a specific section is given by:
\[ P(\text{landing on any letter}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} \]
If we treat all sections (the letters H, O, N, E, S, T) as favorable outcomes, we actually have:
- Number of favorable outcomes = 6 (since there are 6 letters)
- Total number of outcomes = 6 (again, since there are also 6 sections)
Thus, the probability of landing on any letter is:
\[ P = \frac{6}{6} = 1 \]
But since we are asked specifically about landing on an unshaded section, and we have determined all sections are equally viable and none specified as unshaded, if we interpret this to mean there are 6 chances and if none are shaded or not mentioned, any letter is acceptable.
If we assume "unshaded" means we're looking for any of the letters, then the question could imply that all sections are unshaded. Thus a probability of landing on an unshaded section would be:
- The options provided include:
A (3), B (1/3), C (1/6), D (1/2)
Since **C (1/6)** considers landing on each letter showing a fraction of total sections would be the most accurate assumption.
So, indeed, the overall probability of landing on an unshaded section should really evaluate all letters equally and might just probably yield:
**Answer: C (1/6)**