Final answer:
To find the conditional probability of being a 9th grader given a preference for fishing, calculate the joint probability (14.5%) and divide it by the total probability of preferring fishing (43.3%). The answer is approximately 33.5%.
Step-by-step explanation:
The question asks us to find the probability that a student is in the 9th grade, given that fishing is their favorite leisure activity. This is a conditional probability problem, and we can solve it using the provided data.
We are given the percentages of students in each grade level who list fishing as their favorite leisure activity and their respective student population percentages. For the 6th grade, it is 38% of the total and 48% of them prefer fishing. For the 9th grade, it is 29% of the total and 50% of them prefer fishing. For the 11th grade, it is 33% of the total and 32% of them prefer fishing.
To calculate the conditional probability, we need to find the joint probability of being a 9th grader and preferring fishing, and then divide it by the probability of preferring fishing regardless of grade. The joint probability for 9th grade is (0.29)(0.5) = 0.145 or 14.5%. The total probability of preferring fishing, we already have as 43.3%.