To answer your questions about the probability of selecting a student with hazel eyes, we'll need to know two key pieces of information: the total number of students surveyed and how many of those students have hazel eyes.
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Calculating the Probability as a Fraction: If you have the number of students with hazel eyes (let's denote this as \( H \)) and the total number of students surveyed (let's denote this as \( T \)), the probability \( P \) of selecting a student with hazel eyes can be calculated using the formula:
\[ P(\text{hazel eyes}) = \frac{H}{T} \]
To express this probability in simplest form, you would reduce the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
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Assessing Likelihood: In Dale's survey, choosing the response about the likelihood of selecting a student with hazel eyes will depend on the proportion of students with hazel eyes relative to the total.
- If the fraction \( \frac{H}{T} \) is high (like \( \frac{1}{2} \) or greater), you would choose "Likely."
- If it's low (like \( \frac{1}{10} \) or less), you would select "Unlikely."
- If it’s around \( \frac{1}{4} \) to \( \frac{3}{4} \), you would choose "Neither likely nor unlikely."
- If every student has hazel eyes, you would choose "Certain."
Please provide the specific numbers for students with hazel eyes and the total students if you would like numerical answers for the probability.