In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many peop

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Question: In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many people like either tea or coffee?

Options:

Correct Answer: 60

Solution:

Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is: (Tea + Coffee - Both) = 40 + 30 - 10 = 60.

In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many people like either tea or coffee?

In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many people like either tea or coffee?

Step 1: Identify the number of people who like tea. This is given as 40.
Step 2: Identify the number of people who like coffee. This is given as 30.
Step 3: Identify the number of people who like both tea and coffee. This is given as 10.
Step 4: Use the principle of inclusion-exclusion to find the total number of people who like either tea or coffee. The formula is: (Number of tea lovers) + (Number of coffee lovers) - (Number of people who like both).
Step 5: Plug in the numbers: 40 (tea) + 30 (coffee) - 10 (both) = 60.
Step 6: Conclude that 60 people like either tea or coffee.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of two sets by subtracting the size of their intersection.