In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How

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Question: In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How many people like neither sports nor music?

Options:

Correct Answer: 30

Solution:

Using inclusion-exclusion, the number of people who like either is 90 + 60 - 30 = 120, so those who like neither is 150 - 120 = 30.

In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How many people like neither sports nor music?

In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How many people like neither sports nor music?

Step 1: Start with the total number of people surveyed, which is 150.
Step 2: Identify how many people like sports, which is 90.
Step 3: Identify how many people like music, which is 60.
Step 4: Identify how many people like both sports and music, which is 30.
Step 5: Use the inclusion-exclusion principle to find the number of people who like either sports or music. This is calculated as: 90 (like sports) + 60 (like music) - 30 (like both) = 120.
Step 6: To find the number of people who like neither sports nor music, subtract the number of people who like either from the total number of people surveyed: 150 - 120 = 30.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of multiple sets by accounting for overlaps.
Set Theory – The study of collections of objects, which in this case are people who like sports and music.
Basic Arithmetic – The fundamental operations of addition and subtraction used to derive the final answer.