In a class, 50 student play cricket, 20 play hockey, 10 play both the games, then the no. of students playing at least one game is:
Explanation
This problem can be easily solved using the fundamental principle of Set Theory (Inclusion-Exclusion Principle) or by using a Venn diagram.
Step 1: Identify given data
Let:
From the question in image_218a96.png, we have:
Total students playing cricket: n(C)=50
Total students playing hockey: n(H)=20
Students playing both games: n(C∩H)=10
Step 2: Apply the Set Theory formula
The phrase "at least one game" refers to the union of the two sets, which is represented mathematically as n(C∪H).
The formula for the union of two sets is:
n(C∪H)=n(C)+n(H)−n(C∩H)
Step 3: Calculate the final answer
Substitute the values into the formula:
n(C∪H)=50+20−10
n(C∪H)=70−10
n(C∪H)=60
Conclusion
The number of students playing at least one game is 60.
Correct Option: (b) 60
