To determine the probability of landing on an unshaded section when spinning the spinner labeled with the letters of the word "HONEST," we first need to identify the total number of segments and how many of those are unshaded.
The word "HONEST" has 6 unique letters: H, O, N, E, S, and T. If we assume that all segments are unshaded (since no information about shaded sections was given), then all segments are included in the sample space.
The total number of segments = 6 (H, O, N, E, S, T).
Since we don't know if any of these segments are shaded based on the problem statement (it only gives information about the wheel divided into segments), let's assume that none are shaded for the simplest calculation.
The probability of landing on an unshaded section is given by the formula:
\[ P(\text{unshaded}) = \frac{\text{Number of unshaded sections}}{\text{Total number of sections}} \]
If we assume all segments (6 total) are unshaded:
- Number of unshaded sections = 6
- Total number of sections = 6
Thus,
\[ P(\text{unshaded}) = \frac{6}{6} = 1 \]
However, none of the responses provided (1/3, 1/6, 3, 12) shows probability 1. This indicates that there may be a misunderstanding or lack of clarity regarding unshaded sections in the problem.
If we instead consider some segments are unshaded and others are shaded, please provide additional information about which segments are shaded.
If assuming that 3 out of 6 segments are unshaded were considered, that would result in:
\[ P(\text{unshaded}) = \frac{3}{6} = \frac{1}{2} \]
But none of the choices reflect that either.
Given only the choices of responses, if we simplify to the smallest fraction, a common error should also be avoided.
Hence, based on your provided options, picking Start Fraction 1 over 6 End Fraction is indicative of sampling from a limited number (1 unshaded section out of 6 if we're erroneously dividing again). It would be necessary to clarify about shaded sections.
In conclusion, if all sections are unshaded, it would be 1, and within your responses, it does not match exactly; otherwise, without information to create a correct choice, help impede decisive choice. Without clear direction about shaded/unshaded division, assumptions heavily change numbers.
Let’s say if we concluded on 2 segments shaded,
Final suggests with provided choices:
- Option of Start Fraction 1 over 6 End Fraction would be mistakenly using 1 shaded, 6 total hence = unshaded possibly.
Please ensure that the question is properly understood or clarified on sections.