If 100 people were surveyed and 70 like pizza, 50 like pasta, and 20 like both,

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Question: If 100 people were surveyed and 70 like pizza, 50 like pasta, and 20 like both, how many like neither?

Options:

Correct Answer: 30

Solution:

Using inclusion-exclusion, the number of people who like either is 70 + 50 - 20 = 100, so 100 - 100 = 0 like neither.

If 100 people were surveyed and 70 like pizza, 50 like pasta, and 20 like both, how many like neither?

If 100 people were surveyed and 70 like pizza, 50 like pasta, and 20 like both, how many like neither?

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.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of multiple sets by accounting for overlaps.
Set Theory – The study of collections of objects, which in this case are people who like pizza and pasta.