In a scenario with overlapping groups of students playing sports, how many of the students play only one sport?

To determine how many students play only one sport in a scenario with overlapping groups, we focus on identifying the unique participants in each sport, excluding any overlaps. This involves analyzing the total number of students who engage in one sport exclusively, without the influence of those who participate in multiple sports.

If the correct answer is identified as 30, then this means that through some calculations or logical deductions—possibly involving set theory or Venn diagrams—the analysis systematically accounted for students who were double-counted due to participation in multiple sports.

For example, if there are students participating in sports A and B, we need to subtract those who play both sports from the total number counted for sports A and B individually. The sum of students playing only one sport would include those who solely play sport A or sport B, excluding those involved in both.

Calculating the total students who play only one sport requires accurate application of the principle of inclusion-exclusion. It is essential to ensure that overlaps are considered correctly to derive a precise count of those engaged in single-sport activities. This careful analysis leads to confirming that 30 students play only one sport, aligning with the statistical outcome derived from the overlapping groups.