In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like bo
Practice Questions
Q1
In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like both. How many people like neither genre?
30
60
90
120
Questions & Step-by-Step Solutions
In a survey of 150 people, 90 like rock music, 60 like pop music, and 30 like both. How many people like neither genre?
Step 1: Identify the total number of people surveyed, which is 150.
Step 2: Identify how many people like rock music, which is 90.
Step 3: Identify how many people like pop music, which is 60.
Step 4: Identify how many people like both rock and pop music, which is 30.
Step 5: Use the inclusion-exclusion principle to find the number of people who like at least one genre: Add the number of rock and pop music lovers, then subtract those who like both. This is calculated as 90 (rock) + 60 (pop) - 30 (both) = 120.
Step 6: To find the number of people who like neither genre, subtract the number of people who like at least one genre from the total number of people surveyed: 150 (total) - 120 (like at least one) = 30.
