Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we can use the principle of Inclusion-Exclusion. Here's a step-by-step explanation:
1. Identify the Total Number of Tables:
- The restaurant has a total of 60 tables.
2. Count the Round Tables and Window Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
3. Identify Tables that Meet Both Conditions:
- There are 6 tables that are both round and located by the window.
4. Use the Inclusion-Exclusion Principle:
- To avoid double-counting the tables that are both round and by the window, we use the formula:
[tex]\[
\text{Number of round or window tables} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round and window tables})
\][/tex]
- Substituting the values:
[tex]\[
\text{Number of round or window tables} = 38 + 13 - 6 = 45
\][/tex]
5. Calculate the Probability:
- The probability that a customer will be seated at a round table or by the window is the number of favorable outcomes (round or window tables) divided by the total number of tables:
[tex]\[
\text{Probability} = \frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is 0.75, which corresponds to the answer:
B. [tex]\(\frac{45}{60}\)[/tex]
1. Identify the Total Number of Tables:
- The restaurant has a total of 60 tables.
2. Count the Round Tables and Window Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
3. Identify Tables that Meet Both Conditions:
- There are 6 tables that are both round and located by the window.
4. Use the Inclusion-Exclusion Principle:
- To avoid double-counting the tables that are both round and by the window, we use the formula:
[tex]\[
\text{Number of round or window tables} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round and window tables})
\][/tex]
- Substituting the values:
[tex]\[
\text{Number of round or window tables} = 38 + 13 - 6 = 45
\][/tex]
5. Calculate the Probability:
- The probability that a customer will be seated at a round table or by the window is the number of favorable outcomes (round or window tables) divided by the total number of tables:
[tex]\[
\text{Probability} = \frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is 0.75, which corresponds to the answer:
B. [tex]\(\frac{45}{60}\)[/tex]
