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A group of friends consists of 5 people who play football, 4 who play basketball

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Question: A group of friends consists of 5 people who play football, 4 who play basketball, and 2 who play both. How many friends play only one sport?

Options:

  1. 5
  2. 7
  3. 9
  4. 11

Correct Answer: 7

Solution:

To find the number of friends who play only one sport, we calculate: (Football only + Basketball only) = (5 - 2) + (4 - 2) = 3 + 2 = 5.

A group of friends consists of 5 people who play football, 4 who play basketball

Practice Questions

Q1
A group of friends consists of 5 people who play football, 4 who play basketball, and 2 who play both. How many friends play only one sport?
  1. 5
  2. 7
  3. 9
  4. 11

Questions & Step-by-Step Solutions

A group of friends consists of 5 people who play football, 4 who play basketball, and 2 who play both. How many friends play only one sport?
  • Step 1: Identify the total number of friends who play football, which is 5.
  • Step 2: Identify the total number of friends who play basketball, which is 4.
  • Step 3: Identify the number of friends who play both sports, which is 2.
  • Step 4: Calculate the number of friends who play only football by subtracting those who play both from the total football players: 5 - 2 = 3.
  • Step 5: Calculate the number of friends who play only basketball by subtracting those who play both from the total basketball players: 4 - 2 = 2.
  • Step 6: Add the number of friends who play only football and only basketball: 3 + 2 = 5.
  • Set Theory – Understanding the relationships between different groups, specifically how to calculate the number of unique members in overlapping sets.
  • Inclusion-Exclusion Principle – Applying the principle to avoid double counting individuals who belong to multiple categories.
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