In a group of 50 people, 30 like football, 25 like basketball, and 10 like both.

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Question: In a group of 50 people, 30 like football, 25 like basketball, and 10 like both. How many people like neither sport?

Options:

Correct Answer: 15

Solution:

The number of people who like at least one sport is 30 + 25 - 10 = 45. Therefore, those who like neither sport is 50 - 45 = 5.

In a group of 50 people, 30 like football, 25 like basketball, and 10 like both. How many people like neither sport?

In a group of 50 people, 30 like football, 25 like basketball, and 10 like both. How many people like neither sport?

Step 1: Identify the total number of people in the group, which is 50.
Step 2: Identify how many people like football, which is 30.
Step 3: Identify how many people like basketball, which is 25.
Step 4: Identify how many people like both sports, which is 10.
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 30 + 25 - 10 = 45.
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: 50 - 45 = 5.

Set Theory – Understanding how to calculate the union and intersection of sets to determine the total number of unique individuals in overlapping groups.
Inclusion-Exclusion Principle – Applying the principle to avoid double counting individuals who belong to both groups.