Question

compound probabilities - overlapping events

an office has 150 employees. 70 employees drink coffee, 43 drink tea, and 20 drink both. what is the probability that a random employee drinks coffee or tea?

\\(p(\text{coffee or tea}) = \quad\\%\\)

round your answer to the nearest whole percent.

Explanation:

Calculate the number of employees who drink coffee or tea

$$ n(\text{Coffee} \cup \text{Tea}) = n(\text{Coffee}) + n(\text{Tea}) - n(\text{Coffee} \cap \text{Tea}) $$

$$ n(\text{Coffee} \cup \text{Tea}) = 70 + 43 - 20 = 93 $$

Calculate the probability

$$ P(\text{Coffee or Tea}) = \frac{n(\text{Coffee} \cup \text{Tea})}{\text{Total employees}} = \frac{93}{150} = 0.62 $$

Convert to percentage

$$ 0.62 \times 100\% = 62\% $$

Answer:

An office has 150 employees. 70 employees drink coffee, 43 drink tea, and 20 drink both. What is the probability that a random employee drinks coffee or tea?

\(P(\text{Coffee or Tea}) =\) <blank>62</blank>%