In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?
35
Employees: Calculating the Percentage Who Drink Neither Tea Nor Coffee
This problem involves percentages and can be solved using the principle of inclusion-exclusion, which is often visualized with Venn diagrams. We are given the percentage of employees who drink coffee, tea, and both. Our goal is to find the percentage of employees who drink neither.
Percentage: Understanding the Given Information
Let's denote the set of employees who drink coffee as 'C' and those who drink tea as 'T'. We are provided with the following percentages:
- Coffee drinkers (\(P(C)\)): 35%
- Tea drinkers (\(P(T)\)): 40%
- Employees who drink both tea and coffee (\(P(C \cap T)\)): 10%
We need to determine the percentage of employees who drink neither tea nor coffee.
Formula: Applying the Principle of Inclusion-Exclusion
To find the percentage of employees who drink at least one of the two beverages (coffee or tea), we use the formula for the union of two sets:
\(P(C \cup T) = P(C) + P(T) - P(C \cap T)\)
Where:
- \(P(C \cup T)\) represents the percentage of employees who drink coffee or tea or both (at least one).
- \(P(C)\) represents the percentage of employees who drink coffee.
- \(P(T)\) represents the percentage of employees who drink tea.
- \(P(C \cap T)\) represents the percentage of employees who drink both coffee and tea.
Calculating: Employees Who Drink At Least One Beverage
Let's substitute the given values into the formula:
\(P(C \cup T) = 35\% + 40\% - 10\%\)
\(P(C \cup T) = 75\% - 10\%\)
\(P(C \cup T) = 65\%\)
So, 65% of the employees drink at least one of the beverages (coffee or tea).
Neither: Determining the Percentage Who Drink Neither
The total percentage of employees in the company is 100%. If 65% of employees drink at least one beverage, then the remaining percentage must be those who drink neither.
\(\text{Percentage who drink neither} = \text{Total Percentage} - P(C \cup T)\)
\(\text{Percentage who drink neither} = 100\% - 65\%\)
\(\text{Percentage who drink neither} = 35\%\)
Therefore, 35% of the employees drink neither tea nor coffee.
Summary: Final Answer
Based on our calculations, the percentage of employees who drink neither tea nor coffee is 35%.
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