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Answer :
Sure, let's solve the problem step-by-step:
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify the Number of Round Tables and Tables by the Window:
There are 38 round tables.
There are 13 tables located by the window.
3. Identify the Overlap (Round Tables by the Window):
There are 6 round tables that are also by the window. This means these 6 tables are being counted twice when we simply add the round tables and the window tables separately. To avoid this double-counting, we need to subtract them once.
4. Calculate the Number of Unique Tables that are Either Round or by the Window (or Both):
Add the number of round tables to the number of tables by the window, and then subtract the number of tables that are both round and by the window:
[tex]\[
38 \, (\text{round tables}) + 13 \, (\text{tables by the window}) - 6 \, (\text{round tables by the window}) = 45
\][/tex]
5. Calculate the Probability:
The probability that a customer will be seated at a table that is either round or by the window is the number of such tables divided by the total number of tables:
[tex]\[
\frac{45}{60}
\][/tex]
6. Simplify the Fraction:
Simplify [tex]\(\frac{45}{60}\)[/tex] to get [tex]\(\frac{3}{4}\)[/tex], which is equivalent to 0.75.
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which is 0.75. This corresponds to answer choice C, [tex]\(\frac{45}{60}\)[/tex].
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify the Number of Round Tables and Tables by the Window:
There are 38 round tables.
There are 13 tables located by the window.
3. Identify the Overlap (Round Tables by the Window):
There are 6 round tables that are also by the window. This means these 6 tables are being counted twice when we simply add the round tables and the window tables separately. To avoid this double-counting, we need to subtract them once.
4. Calculate the Number of Unique Tables that are Either Round or by the Window (or Both):
Add the number of round tables to the number of tables by the window, and then subtract the number of tables that are both round and by the window:
[tex]\[
38 \, (\text{round tables}) + 13 \, (\text{tables by the window}) - 6 \, (\text{round tables by the window}) = 45
\][/tex]
5. Calculate the Probability:
The probability that a customer will be seated at a table that is either round or by the window is the number of such tables divided by the total number of tables:
[tex]\[
\frac{45}{60}
\][/tex]
6. Simplify the Fraction:
Simplify [tex]\(\frac{45}{60}\)[/tex] to get [tex]\(\frac{3}{4}\)[/tex], which is equivalent to 0.75.
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which is 0.75. This corresponds to answer choice C, [tex]\(\frac{45}{60}\)[/tex].
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