In a group of 200 people, 120 like football, 80 like basketball, and 50 like bot

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Question: In a group of 200 people, 120 like football, 80 like basketball, and 50 like both. How many people like neither sport?

Options:

Correct Answer: 70

Solution:

The number of people who like at least one sport is: 120 + 80 - 50 = 150. Therefore, those who like neither is: 200 - 150 = 50.

In a group of 200 people, 120 like football, 80 like basketball, and 50 like both. How many people like neither sport?

In a group of 200 people, 120 like football, 80 like basketball, and 50 like both. How many people like neither sport?

Step 1: Identify the total number of people in the group, which is 200.
Step 2: Identify how many people like football, which is 120.
Step 3: Identify how many people like basketball, which is 80.
Step 4: Identify how many people like both sports, which is 50.
Step 5: Calculate the number of people who like at least one sport using the formula: (people who like football) + (people who like basketball) - (people who like both). This gives us: 120 + 80 - 50 = 150.
Step 6: To find out how many people like neither sport, subtract the number of people who like at least one sport from the total number of people: 200 - 150 = 50.

Set Theory – Understanding how to calculate the union of two sets and the principle of inclusion-exclusion.
Venn Diagrams – Visualizing the relationships between different groups to solve problems involving overlaps.