If 70% of students play football, 50% play basketball, and 20% play both, what p

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Question: If 70% of students play football, 50% play basketball, and 20% play both, what percentage of students play either football or basketball?

Options:

100%
90%
80%
70%

Correct Answer: 90%

Solution:

Using inclusion-exclusion, the percentage of students who play either sport is 70% + 50% - 20% = 100%.

If 70% of students play football, 50% play basketball, and 20% play both, what p

Practice Questions

If 70% of students play football, 50% play basketball, and 20% play both, what percentage of students play either football or basketball?

100%
90%
80%
70%

Questions & Step-by-Step Solutions

If 70% of students play football, 50% play basketball, and 20% play both, what percentage of students play either football or basketball?

Step 1: Understand that 70% of students play football.
Step 2: Understand that 50% of students play basketball.
Step 3: Understand that 20% of students play both football and basketball.
Step 4: To find the percentage of students who play either football or basketball, we use the inclusion-exclusion principle.
Step 5: Add the percentage of students who play football (70%) to the percentage of students who play basketball (50%).
Step 6: This gives us 70% + 50% = 120%.
Step 7: Now, subtract the percentage of students who play both sports (20%) from this total.
Step 8: So, we calculate 120% - 20% = 100%.
Step 9: Therefore, 100% of students play either football or basketball.

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.

If 70% of students play football, 50% play basketball, and 20% play both, what p

What’s inside this PDF?

If 70% of students play football, 50% play basketball, and 20% play both, what p

Practice Questions

Questions & Step-by-Step Solutions

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