To find the probability that a student is in the 12th grade given that they prefer soccer, we need to have the relevant data (like the total number of students who prefer soccer and how many of those are in the 12th grade). However, since no such data is provided in your question, I will guide you through the conceptual process.
The conditional probability formula is:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
where:
- \( A \) is the event that the student is in the 12th grade,
- \( B \) is the event that the student prefers soccer,
- \( P(A|B) \) is the probability that a student is in the 12th grade given that they prefer soccer,
- \( P(A \cap B) \) is the probability that a student is both in the 12th grade and prefers soccer,
- \( P(B) \) is the probability that a student prefers soccer.
Without numerical data, it’s impossible to determine the exact probability. If you could provide the totals or any counts from a survey or sample, I would be able to assist you further in making the calculation.
Given only the options provided, it seems to represent multiple-choice answers, but without context and data, it's impossible to choose one accurately. If you have any specific numbers or ratios associated with the preferences and grades, please share them, and I can assist you with the calculations.