If 60% of students in a school are enrolled in sports, 40% in arts, and 10% in b

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Question: If 60% of students in a school are enrolled in sports, 40% in arts, and 10% in both, what percentage are enrolled in either?

Options:

Correct Answer: 90%

Solution:

Using inclusion-exclusion, the percentage enrolled in either is 60% + 40% - 10% = 90%.

If 60% of students in a school are enrolled in sports, 40% in arts, and 10% in both, what percentage are enrolled in either?

If 60% of students in a school are enrolled in sports, 40% in arts, and 10% in both, what percentage are enrolled in either?

Step 1: Identify the percentage of students enrolled in sports, which is 60%.
Step 2: Identify the percentage of students enrolled in arts, which is 40%.
Step 3: Identify the percentage of students enrolled in both sports and arts, which is 10%.
Step 4: Use the inclusion-exclusion principle to find the percentage of students enrolled in either sports or arts. This means you add the percentages of students in sports and arts, then subtract the percentage of students in both.
Step 5: Calculate: 60% (sports) + 40% (arts) - 10% (both) = 90%.
Step 6: Conclude that 90% of students are enrolled in either sports or arts.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of two sets by adding the sizes of the individual sets and subtracting the size of their intersection.