Question

At Cityville High School, 38% of the students participate in sports, 32% of the students participate in academic clubs, and 20% of the students participate in both sports and academic clubs.

What is the proportion of students who participate in either sports or academic clubs, while providing an exact answer?

Answer 1

To calculate the proportion of students at Cityville High School who participate in either sports or academic clubs, we use the principle of inclusion-exclusion: 38% (sports) + 32% (academic clubs) - 20% (both). The result is 50%, meaning half of the students are involved in at least one of these activities.

Step-by-step explanation:

To find the proportion of students who participate in either sports or academic clubs at Cityville High School, we use the principle of inclusion-exclusion. To do this, we add the proportion of students who participate in sports to the proportion who participate in academic clubs and then subtract the proportion who participate in both. So, it would be calculated as follows:

• Percentage participating in sports = 38%
• Percentage participating in academic clubs = 32%
• Percentage participating in both = 20%

The proportion of students participating in either sports or academic clubs is 38% + 32% - 20% = 50%. Therefore, half of the students participate in at least one of the two activities.