If 60% of students play cricket, 50% play football, and 30% play both, what perc

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Question: If 60% of students play cricket, 50% play football, and 30% play both, what percentage of students play either cricket or football?

Options:

Correct Answer: 80%

Solution:

Using inclusion-exclusion, the percentage playing either is 60% + 50% - 30% = 80%.

If 60% of students play cricket, 50% play football, and 30% play both, what percentage of students play either cricket or football?

If 60% of students play cricket, 50% play football, and 30% play both, what percentage of students play either cricket or football?

Step 1: Understand that 60% of students play cricket.
Step 2: Understand that 50% of students play football.
Step 3: Understand that 30% of students play both cricket and football.
Step 4: To find the percentage of students who play either cricket or football, we use the formula: (Percentage playing cricket) + (Percentage playing football) - (Percentage playing both).
Step 5: Substitute the values into the formula: 60% + 50% - 30%.
Step 6: Calculate the result: 60 + 50 = 110, then 110 - 30 = 80.
Step 7: Conclude that 80% of students play either cricket or football.

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.