In a survey of 150 people, 90 like soccer, 60 like basketball, and 30 like both.

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Question: In a survey of 150 people, 90 like soccer, 60 like basketball, and 30 like both. How many people like neither sport?

Options:

Correct Answer: 30

Solution:

The number of people who like neither sport is total - (|Soccer| + |Basketball| - |Both|) = 150 - (90 + 60 - 30) = 30.

In a survey of 150 people, 90 like soccer, 60 like basketball, and 30 like both. How many people like neither sport?

In a survey of 150 people, 90 like soccer, 60 like basketball, and 30 like both. How many people like neither sport?

Step 1: Identify the total number of people surveyed, which is 150.
Step 2: Identify how many people like soccer, which is 90.
Step 3: Identify how many people like basketball, which is 60.
Step 4: Identify how many people like both sports, which is 30.
Step 5: Use the formula to find the number of people who like at least one sport: Total - (Soccer + Basketball - Both).
Step 6: Substitute the numbers into the formula: 150 - (90 + 60 - 30).
Step 7: Calculate the sum inside the parentheses: 90 + 60 = 150, then 150 - 30 = 120.
Step 8: Now subtract this result from the total: 150 - 120 = 30.
Step 9: The result, 30, is the number of people who like neither sport.

Set Theory – Understanding how to calculate the union and intersection of sets to find the total number of unique elements.
Inclusion-Exclusion Principle – Applying the principle to avoid double counting individuals who like both sports.