Question

Employees at an office were surveyed about what types of hot beverages they drank that day. It was found that 50% of them drank coffee and 25% drank tea. The survey showed that 10% of the employees drank both coffee and tea.

Options:
a) 15% of employees drank neither coffee nor tea.
b) 40% of employees drank neither coffee nor tea.
c) 25% of employees drank neither coffee nor tea.
d) 30% of employees drank neither coffee nor tea.

Answer 1

Using the principle of inclusion-exclusion, 50% of the employees drank coffee, 25% drank tea, and 10% drank both. By subtracting the percentage drinking both from the sum of individuals drinking each beverage, we find that 65% drank coffee or tea. Thus, 35% drank neither, which doesn't match the provided options, indicating an error in the question.

Step-by-step explanation:

Let's use the information given to solve the problem. We know that 50% of the employees drank coffee, 25% drank tea, and 10% drank both coffee and tea.

To find out the percentage of employees who drank neither coffee nor tea, we can use the principle of inclusion-exclusion. The principle tells us to add the individual percentages and subtract the intersection (both).

The calculation would be:

• Total drinking coffee or tea = Percentage drinking coffee + Percentage drinking tea - Percentage drinking both
• Total drinking coffee or tea = 50% + 25% - 10%
• Total drinking coffee or tea = 65%

This means that 65% of the employees drank either coffee or tea. Since the survey includes all employees, the rest of them did not drink coffee or tea.

The percentage of employees that drank neither coffee nor tea would be:

• 100% - Total drinking coffee or tea
• 100% - 65%
• 35%% of employees drank neither coffee nor tea

Since 35% does not match any of the provided options (a, b, c, or d), there might be an error in the options provided for the question.