If 80% of a population likes tea, 60% likes coffee, and 30% likes both, what per

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Question: If 80% of a population likes tea, 60% likes coffee, and 30% likes both, what percentage likes at least one of the two?

Options:

Correct Answer: 80%

Solution:

Using inclusion-exclusion, the percentage liking at least one is 80% + 60% - 30% = 110%, which is capped at 100%.

If 80% of a population likes tea, 60% likes coffee, and 30% likes both, what percentage likes at least one of the two?

If 80% of a population likes tea, 60% likes coffee, and 30% likes both, what percentage likes at least one of the two?

Step 1: Identify the percentage of people who like tea, which is 80%.
Step 2: Identify the percentage of people who like coffee, which is 60%.
Step 3: Identify the percentage of people who like both tea and coffee, which is 30%.
Step 4: Use the inclusion-exclusion principle to find the percentage of people who like at least one of the two drinks. This is done by adding the percentage of tea lovers and coffee lovers, then subtracting the percentage of people who like both.
Step 5: Calculate: 80% (tea) + 60% (coffee) - 30% (both) = 110%.
Step 6: Since percentages cannot exceed 100%, we cap the result at 100%.
Step 7: Conclude that 100% of the population likes at least one of the two drinks.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of two sets by adding the sizes of the individual sets and subtracting the size of their intersection.
Percentage Calculation – Understanding how to interpret and manipulate percentages in the context of set theory.