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Answer :
To solve this problem, we'll use the formula for the probability of either one event or another happening. We're interested in finding the probability that a customer will be seated at either a round table or a table by the window.
Here's how we can think about it step by step:
1. Identify the total number of tables: There are a total of 60 tables in the restaurant.
2. Count the round tables: There are 38 round tables.
3. Count the tables by the window: There are 13 tables located by the window.
4. Identify the overlap (round tables by the window): There are 6 round tables that are also by the window.
5. Use the principle of inclusion and exclusion: To find the number of 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 overlap (tables that are both round and by the window) since they've been counted twice.
- Number of round tables or window tables = Round tables + Window tables - Round tables by the window
- Number of tables = 38 + 13 - 6 = 45
6. Calculate the probability: The probability that a customer will be seated at a round table or by the window is the number of such tables divided by the total number of tables.
- Probability = (Number of round tables or window tables) / Total tables
- Probability = 45 / 60
7. Simplify the fraction:
- 45 divided by 60 is equivalent to 0.75, or simplified as [tex]\(\frac{45}{60}\)[/tex] = [tex]\(\frac{3}{4}\)[/tex].
Thus, the probability that a customer will be seated at a round table or by the window is 0.75, which corresponds to answer choice C, [tex]\(\frac{45}{60}\)[/tex].
Here's how we can think about it step by step:
1. Identify the total number of tables: There are a total of 60 tables in the restaurant.
2. Count the round tables: There are 38 round tables.
3. Count the tables by the window: There are 13 tables located by the window.
4. Identify the overlap (round tables by the window): There are 6 round tables that are also by the window.
5. Use the principle of inclusion and exclusion: To find the number of 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 overlap (tables that are both round and by the window) since they've been counted twice.
- Number of round tables or window tables = Round tables + Window tables - Round tables by the window
- Number of tables = 38 + 13 - 6 = 45
6. Calculate the probability: The probability that a customer will be seated at a round table or by the window is the number of such tables divided by the total number of tables.
- Probability = (Number of round tables or window tables) / Total tables
- Probability = 45 / 60
7. Simplify the fraction:
- 45 divided by 60 is equivalent to 0.75, or simplified as [tex]\(\frac{45}{60}\)[/tex] = [tex]\(\frac{3}{4}\)[/tex].
Thus, the probability that a customer will be seated at a round table or by the window is 0.75, which corresponds to answer choice C, [tex]\(\frac{45}{60}\)[/tex].
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