Geometry

Question Analysis
This question involves analyzing a Venn Diagram to calculate the probability of a compound event with specific conditions.
The main focus is on correctly identifying and summing up the relevant regions in the Venn Diagram that represent students participating in the math club or the basketball team but not the choir, and then determining the probability.

Key Concept Explanation
The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes.
For the event of participating in the math club or the basketball team but not the choir, the favorable outcomes are the students in the regions “only M”, “only B”, and “M and B only”.
The total number of outcomes is the sum of all the numbers in the Venn Diagram, representing the total number of students involved in these activities.

Step - by - Step Solution
Identify the relevant regions: The regions representing students participating in the math club or the basketball team but not the choir are “only M” (20 students), “only B” (14 students), and “M and B only” (9 students).
Calculate the number of favorable outcomes: Sum up the number of students in these regions: .
Calculate the total number of students: Add up all the numbers in the Venn Diagram:

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