Geometry

Question Analysis
This question involves using Venn Diagrams to calculate the probability of a compound event.
The main focus is on understanding the principle of inclusion - exclusion when dealing with the union of two sets in the context of probability.

Key Concept Explanation
For two events A and B, the probability of A or B (P(A ∪ B)) is given by P(A) + P(B) - P(A ∩ B).
In the context of Venn Diagrams, the union of two sets (like students who play basketball or soccer) is found by adding the number of elements in each set and subtracting the number of elements in their intersection to avoid double - counting.

Step - by - Step Solution
First, find the total number of students who play either basketball or soccer.
Using the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B), where n(A) = 30 (basketball players), n(B) = 25 (soccer players), and n(A ∩ B)...