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Answer :
To solve the problem and find 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 solution:
1. Identify Total Numbers:
- Total tables in the restaurant: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
2. Find the Probability of Round or Window Table:
- We want the probability of a table being either round or by the window, but we must be careful not to double-count the tables that are both round and by the window.
3. Apply the Inclusion-Exclusion Principle:
- First, add the number of round tables and the number of tables by the window:
- Round tables + Window tables = 38 + 13 = 51
- Subtract the tables that are double-counted (round and by the window):
- Total round or window tables = 51 - 6 = 45
4. Calculate the Probability:
- The probability that a customer will be seated at a round table or by the window is the number of round or window tables divided by the total number of tables.
- Probability = Favorable outcomes / Total outcomes = 45 / 60 = 0.75
5. Conclusion:
- The probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
- Thus, the correct answer is [tex]\(\frac{45}{60}\)[/tex], corresponding to option C.
1. Identify Total Numbers:
- Total tables in the restaurant: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
2. Find the Probability of Round or Window Table:
- We want the probability of a table being either round or by the window, but we must be careful not to double-count the tables that are both round and by the window.
3. Apply the Inclusion-Exclusion Principle:
- First, add the number of round tables and the number of tables by the window:
- Round tables + Window tables = 38 + 13 = 51
- Subtract the tables that are double-counted (round and by the window):
- Total round or window tables = 51 - 6 = 45
4. Calculate the Probability:
- The probability that a customer will be seated at a round table or by the window is the number of round or window tables divided by the total number of tables.
- Probability = Favorable outcomes / Total outcomes = 45 / 60 = 0.75
5. Conclusion:
- The probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
- Thus, the correct answer is [tex]\(\frac{45}{60}\)[/tex], corresponding to option C.
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