Answer :
To solve this problem and determine the probability that a customer will be seated at a round table or by the window, we'll use the principle of inclusion-exclusion.
1. Total number of tables: There are 60 tables in the restaurant.
2. Number of round tables: 38 tables are round.
3. Number of tables by the window: 13 tables are located by the window.
4. Number of round tables by the window: Among the 13 tables by the window, 6 are also round.
Now, to find the probability that a customer will be seated at either a round table or a table by the window, we need to calculate the total number of tables that are either round or by the window. To do this, we apply the principle of inclusion-exclusion:
- Start by adding the number of round tables and the number of tables by the window:
[tex]\( 38 \text{ round tables} + 13 \text{ tables by the window} = 51 \text{ tables} \)[/tex].
- However, the tables that are both round and by the window are counted twice in this sum. So, we subtract the number of round tables by the window to correct this double-counting:
[tex]\( 51 - 6 = 45 \text{ tables} \)[/tex].
This means there are 45 tables that are either round or by the window.
5. Calculate the probability:
To find the probability, divide the number of tables that are either round or by the window by the total number of tables:
[tex]\( \text{Probability} = \frac{45}{60} \)[/tex].
6. Simplify the fraction:
Simplifying [tex]\( \frac{45}{60} \)[/tex] gives us [tex]\( \frac{3}{4} \)[/tex] or 0.75.
So, the probability that a customer will be seated at a round table or by the window is [tex]\( \frac{45}{60} \)[/tex].
The correct answer is:
C. [tex]\(\frac{45}{60}\)[/tex]
1. Total number of tables: There are 60 tables in the restaurant.
2. Number of round tables: 38 tables are round.
3. Number of tables by the window: 13 tables are located by the window.
4. Number of round tables by the window: Among the 13 tables by the window, 6 are also round.
Now, to find the probability that a customer will be seated at either a round table or a table by the window, we need to calculate the total number of tables that are either round or by the window. To do this, we apply the principle of inclusion-exclusion:
- Start by adding the number of round tables and the number of tables by the window:
[tex]\( 38 \text{ round tables} + 13 \text{ tables by the window} = 51 \text{ tables} \)[/tex].
- However, the tables that are both round and by the window are counted twice in this sum. So, we subtract the number of round tables by the window to correct this double-counting:
[tex]\( 51 - 6 = 45 \text{ tables} \)[/tex].
This means there are 45 tables that are either round or by the window.
5. Calculate the probability:
To find the probability, divide the number of tables that are either round or by the window by the total number of tables:
[tex]\( \text{Probability} = \frac{45}{60} \)[/tex].
6. Simplify the fraction:
Simplifying [tex]\( \frac{45}{60} \)[/tex] gives us [tex]\( \frac{3}{4} \)[/tex] or 0.75.
So, the probability that a customer will be seated at a round table or by the window is [tex]\( \frac{45}{60} \)[/tex].
The correct answer is:
C. [tex]\(\frac{45}{60}\)[/tex]
