Question

select the correct answer.
a restaurant has a total of 60 tables. of those tables, 38 are round and 13 are located by the window. there are 6 round tables by the window.
if tables are randomly assigned to customers, what is the probability that a customer will be seated at a round table or by the window?
a. \\(\frac{41}{60}\\)
b. \\(\frac{47}{60}\\)
c. \\(\frac{45}{60}\\)
d. \\(\frac{29}{60}\\)

Explanation:

Step1: Define the probability formula

For non-mutually exclusive events, the probability of event A or event B is given by:
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Step2: Calculate P(round table)

Total tables = 60, round tables = 38
$P(\text{round}) = \frac{38}{60}$

Step3: Calculate P(window table)

Window tables = 13
$P(\text{window}) = \frac{13}{60}$

Step4: Calculate P(round and window)

Round tables by window = 6
$P(\text{round} \cap \text{window}) = \frac{6}{60}$

Step5: Substitute into the formula

$P(\text{round} \cup \text{window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} = \frac{38+13-6}{60} = \frac{45}{60}$

Answer:

C. $\frac{45}{60}$