If 100 people were surveyed and 70 like pizza, 50 like pasta, and 20 like both, how many like neither?
Practice Questions
1 question
Q1
If 100 people were surveyed and 70 like pizza, 50 like pasta, and 20 like both, how many like neither?
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Using inclusion-exclusion, the number of people who like either is 70 + 50 - 20 = 100, so 100 - 100 = 0 like neither.
Questions & Step-by-step Solutions
1 item
Q
Q: If 100 people were surveyed and 70 like pizza, 50 like pasta, and 20 like both, how many like neither?
Solution: Using inclusion-exclusion, the number of people who like either is 70 + 50 - 20 = 100, so 100 - 100 = 0 like neither.
Steps: 7
Step 1: Start with the total number of people surveyed, which is 100.
Step 2: Identify how many people like pizza, which is 70.
Step 3: Identify how many people like pasta, which is 50.
Step 4: Identify how many people like both pizza and pasta, which is 20.
Step 5: Use the inclusion-exclusion principle to find the number of people who like either pizza or pasta. This is calculated as: 70 (like pizza) + 50 (like pasta) - 20 (like both) = 100.
Step 6: To find out how many people like neither pizza nor pasta, subtract the number of people who like either from the total number of people surveyed: 100 (total) - 100 (like either) = 0.
Step 7: Therefore, the number of people who like neither pizza nor pasta is 0.
