In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How

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Question: In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How many people like at least one of the activities?

Options:

Correct Answer: 120

Solution:

Using inclusion-exclusion, the total is 90 + 60 - 30 = 120.

In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How many people like at least one of the activities?

In a survey of 150 people, 90 like sports, 60 like music, and 30 like both. How many people like at least one of the activities?

Step 1: Identify the number of people who like sports. This is 90 people.
Step 2: Identify the number of people who like music. This is 60 people.
Step 3: Identify the number of people who like both sports and music. This is 30 people.
Step 4: To find the total number of people who like at least one activity, use the inclusion-exclusion principle.
Step 5: Add the number of people who like sports (90) and the number of people who like music (60). This gives you 150.
Step 6: Subtract the number of people who like both activities (30) from the total (150).
Step 7: The calculation is 90 + 60 - 30 = 120.
Step 8: Therefore, 120 people like at least one of the activities.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of two or more sets by including the sizes of the individual sets and excluding the sizes of their intersections.