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Answer :
To solve this problem, we are looking to find the probability that a randomly assigned table is round.
Let's break it down step by step:
1. Total number of tables in the restaurant: We are given that the restaurant has 60 tables in total.
2. Number of round tables: Out of those 60 tables, 38 are round.
3. Probability calculation: Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this scenario, the favorable outcome is a table being round, and the total possible outcomes are all the tables.
So the probability [tex]\( P \)[/tex] that a randomly assigned table is round is calculated as follows:
[tex]\[
P(\text{round}) = \frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60}
\][/tex]
4. Simplification: The fraction [tex]\(\frac{38}{60}\)[/tex] simplifies to approximately 0.6333 when converted into a decimal.
Now, let's compare this result to the given answer choices:
- A. [tex]\(\frac{45}{60}\)[/tex]
- B. [tex]\(\frac{47}{60}\)[/tex]
- C. [tex]\(\frac{29}{60}\)[/tex]
- D. [tex]\(\frac{41}{60}\)[/tex]
Converting these fractions to decimals, we see:
- For A: [tex]\(\frac{45}{60} \approx 0.75\)[/tex]
- For B: [tex]\(\frac{47}{60} \approx 0.7833\)[/tex]
- For C: [tex]\(\frac{29}{60} \approx 0.4833\)[/tex]
- For D: [tex]\(\frac{41}{60} \approx 0.6833\)[/tex]
None of these answers directly match our calculated probability of approximately 0.6333. Double-checking everything, it seems there might have been an initial misinterpretation or error in the options provided, indicating that we may need to review the options context or why none aligns.
Let's break it down step by step:
1. Total number of tables in the restaurant: We are given that the restaurant has 60 tables in total.
2. Number of round tables: Out of those 60 tables, 38 are round.
3. Probability calculation: Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this scenario, the favorable outcome is a table being round, and the total possible outcomes are all the tables.
So the probability [tex]\( P \)[/tex] that a randomly assigned table is round is calculated as follows:
[tex]\[
P(\text{round}) = \frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60}
\][/tex]
4. Simplification: The fraction [tex]\(\frac{38}{60}\)[/tex] simplifies to approximately 0.6333 when converted into a decimal.
Now, let's compare this result to the given answer choices:
- A. [tex]\(\frac{45}{60}\)[/tex]
- B. [tex]\(\frac{47}{60}\)[/tex]
- C. [tex]\(\frac{29}{60}\)[/tex]
- D. [tex]\(\frac{41}{60}\)[/tex]
Converting these fractions to decimals, we see:
- For A: [tex]\(\frac{45}{60} \approx 0.75\)[/tex]
- For B: [tex]\(\frac{47}{60} \approx 0.7833\)[/tex]
- For C: [tex]\(\frac{29}{60} \approx 0.4833\)[/tex]
- For D: [tex]\(\frac{41}{60} \approx 0.6833\)[/tex]
None of these answers directly match our calculated probability of approximately 0.6333. Double-checking everything, it seems there might have been an initial misinterpretation or error in the options provided, indicating that we may need to review the options context or why none aligns.
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