Question

In a class, 60% students play cricket, 50% play football, and 30% play both. How many students play at least one sport?

• A. 70%
  
• B. 80%
  
• C. 90%
  
• D. 100%
  

Hint:

Use inclusion-exclusion for problems involving overlapping sets.

Answer 1

The Correct Option is B

- Step 1: Use inclusion-exclusion. For two sets, $|A \cup B| = |A| + |B| - |A \cap B|$.
- Step 2: Assign values. Cricket = 60%, Football = 50%, Both = 30%.
- Step 3: Calculate. At least one = $60 + 50 - 30 = 80%$.
- Step 4: Verify with Venn diagram. Cricket only = $60 - 30 = 30%$, Football only = $50 - 30 = 20%$, Both = 30%. Total = $30 + 20 + 30 = 80%$.
- Step 5: Compare with options. Options: (1) 70%, (2) 80%, (3) 90%, (4) 100%. Matches 80%.
- Step 6: Cross-check. Neither sport = $100 - 80 = 20%$.
- Step 7: Conclusion. Option (2) is correct.