To determine the probability that a randomly assigned table is either a round table or a table by the window, we can follow these steps:
1. Identify the given information:
- Total number of tables: [tex]\(60\)[/tex]
- Number of round tables: [tex]\(38\)[/tex]
- Number of tables by the window: [tex]\(13\)[/tex]
- Number of round tables by the window (overlap): [tex]\(6\)[/tex]
2. Use the principle of inclusion-exclusion:
To find the number of tables that are either round or by the window, we can use the inclusion-exclusion principle. This principle helps in avoiding double-counting of tables that are both round and by the window.
[tex]\[
\text{Number of tables that are either round or by the window} = \text{Number of round tables} + \text{Number of window tables} - \text{Number of round window tables}
\][/tex]
Substituting the given values:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
3. Calculate the probability:
The probability that a randomly assigned table is either round or by the window is the ratio of the number of favorable outcomes (either round or by the window) to the total number of possible outcomes (total tables).
[tex]\[
\text{Probability} = \frac{\text{Number of tables that are either round or by the window}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
4. Simplify the fraction (if required):
The fraction [tex]\(\frac{45}{60}\)[/tex] can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 15:
[tex]\[
\frac{45 \div 15}{60 \div 15} = \frac{3}{4}
\][/tex]
Since the problem provides multiple choices and the answer in the choices does not require simplification, the correct answer from the options given is:
A. [tex]\(\frac{45}{60}\)[/tex]
Thus, the correct answer is [tex]\( A. \frac{45}{60} \)[/tex].
