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?

Solving for Employees Drinking Neither Tea Nor Coffee

This question asks us to find the percentage of employees who do not drink tea and do not drink coffee, given information about those who drink tea, coffee, or both.

Understanding the Given Information

- Percentage of employees who drink coffee = 35%
- Percentage of employees who drink tea = 40%
- Percentage of employees who drink both tea and coffee = 10%

Applying the Inclusion-Exclusion Principle

We can use the principle of inclusion-exclusion to find the percentage of employees who drink at least one of the beverages (tea or coffee).

Let C be the event that an employee drinks coffee.

Let T be the event that an employee drinks tea.

We are given:

- $P(C)=35\%$
- $P(T)=40\%$
- $P(C\cap T)=10\%$ (The percentage who drink both)

The formula for the percentage of employees drinking either tea or coffee or both is:

$$P(C\cup T)=P(C)+P(T)-P(C\cap T)$$

Substituting the given values:

$$P(C\cup T)=35\%+40\%-10\%$$

$$P(C\cup T)=75\%-10\%$$

$$P(C\cup T)=65\%$$

This means 65% of the employees drink either tea or coffee or both.

Calculating the Percentage of Employees Drinking Neither

To find the percentage of employees who drink neither tea nor coffee, we subtract the percentage who drink at least one beverage from the total percentage (100%).

Percentage drinking neither = Total Percentage - Percentage drinking at least one

$$\text{Percentage(Neither)}=100\%-P(C\cup T)$$

$$\text{Percentage(Neither)}=100\%-65\%$$

$$\text{Percentage(Neither)}=35\%$$

Conclusion

Therefore, 35% of the employees drink neither tea nor coffee.