Geometry

Question Analysis
This question requires analyzing a Venn Diagram to calculate the probability of a specific compound event.
The main focus is on correctly identifying the region in the Venn Diagram that represents students participating in basketball and volleyball but not soccer, and then determining the probability based on the number of students in that region and the total number of students.

Key Concept Explanation
The probability formula, where the probability of an event is the number of favorable outcomes divided by the total number of outcomes, is applied here.
The “B and V only” region represents the favorable outcomes, and the sum of all regions in the Venn Diagram gives the total number of outcomes.

Step - by - Step Solution
Identify the number of favorable outcomes: The “B and V only” region has 9 students, which are the ones participating in basketball and volleyball but not soccer.
Calculate the total number of students: Add up all the numbers in the Venn Diagram: