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

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

Options:

  1. 30
  2. 60
  3. 90
  4. 120

Correct Answer: 30

Solution: 

Using inclusion-exclusion, the number of people who like at least one sport is 90 + 60 - 30 = 120. Therefore, those who like neither is 150 - 120 = 30.

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

Practice Questions

Q1
In a survey of 150 people, 90 like basketball, 60 like soccer, and 30 like both. How many like neither sport?
  1. 30
  2. 60
  3. 90
  4. 120

Questions & Step-by-Step Solutions

In a survey of 150 people, 90 like basketball, 60 like soccer, and 30 like both. How many like neither sport?
  • Step 1: Identify the total number of people surveyed, which is 150.
  • Step 2: Identify how many people like basketball, which is 90.
  • Step 3: Identify how many people like soccer, which is 60.
  • Step 4: Identify how many people like both sports, which is 30.
  • Step 5: Use the inclusion-exclusion principle to find the number of people who like at least one sport: Add the number of basketball fans (90) and soccer fans (60), then subtract those who like both (30). This gives us 90 + 60 - 30 = 120.
  • Step 6: To find out how many people like neither sport, subtract the number of people who like at least one sport (120) from the total number of people surveyed (150). This gives us 150 - 120 = 30.
  • Inclusion-Exclusion Principle – A method used to calculate the size of the union of multiple sets by including the sizes of the individual sets and excluding the sizes of their intersections.
  • Set Theory – The study of collections of objects, which in this case are people who like different sports.
  • Basic Arithmetic – The fundamental operations of addition and subtraction used to derive the final answer.
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