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 100 - meter dash or the high jump but not the long jump, and then calculating 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 union of two events (100 - meter dash and high jump), we consider the non - overlapping parts of these events that do not include the long jump region.
The total number of outcomes is the sum of all the numbers in the Venn Diagram.

Step - by - Step Solution
Identify the relevant regions: The regions that represent students participating in the 100 - meter dash or the high jump but not the long jump are “only D” (18 students), “only H” (10 students), and “D and H only” (7 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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