In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How
Practice Questions
Q1
In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How many people like neither sports nor music?
30
60
90
120
Questions & Step-by-Step Solutions
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.
