To find the probability that a student is a senior given that the student voted for an eagle mascot, we can use conditional probability. The formula for conditional probability \( P(A | B) \) is given by:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
Where:
- \( A \) is the event that the student is a senior.
- \( B \) is the event that the student voted for an eagle mascot.
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Calculate \( P(A \cap B) \): This is the probability that a student is both a senior and voted for an eagle. From the table, the number of seniors who voted for an eagle is 55.
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Calculate \( P(B) \): This is the total number of students who voted for an eagle. From the table, the total number of eagle votes is 340.
Next, we plug these values into the conditional probability formula:
\[ P(A | B) = \frac{\text{Number of seniors who voted for eagle}}{\text{Total number of eagle votes}} = \frac{55}{340} \]
Now, simplify the fraction:
\[ P(A | B) = \frac{55 \div 5}{340 \div 5} = \frac{11}{68} \]
Thus, the probability that a student is a senior given that they voted for an eagle mascot is:
\[ \frac{11}{68} \]
So, the final answer is \( \frac{11}{68} \).
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