Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we need to consider the following:
1. Identify the Numbers:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Tables that are both round and by the window: 6
2. Use the Principle of Inclusion-Exclusion:
The probability of a customer being seated at a round table or by the window can be found using the formula for the union of two sets:
[tex]\[
P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window})
\][/tex]
3. Apply the Values:
- The number of round tables is 38.
- The number of window tables is 13.
- However, 6 tables are both round and by the window, so we must subtract these to avoid double-counting.
4. Calculate the Total Favorable Outcomes:
- Total favorable outcomes = Round tables + Window tables - Round and Window tables
- Total favorable outcomes = 38 + 13 - 6 = 45
5. Calculate the Probability:
- Probability = Total favorable outcomes / Total tables
- Probability = 45/60
6. Express the Probability as a Fraction:
- Simplified, this probability is [tex]\(\frac{45}{60} = \frac{3}{4}\)[/tex].
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{3}{4}\)[/tex] or in terms of the choices provided, this corresponds to option B: [tex]\(\frac{45}{60}\)[/tex].
1. Identify the Numbers:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Tables that are both round and by the window: 6
2. Use the Principle of Inclusion-Exclusion:
The probability of a customer being seated at a round table or by the window can be found using the formula for the union of two sets:
[tex]\[
P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window})
\][/tex]
3. Apply the Values:
- The number of round tables is 38.
- The number of window tables is 13.
- However, 6 tables are both round and by the window, so we must subtract these to avoid double-counting.
4. Calculate the Total Favorable Outcomes:
- Total favorable outcomes = Round tables + Window tables - Round and Window tables
- Total favorable outcomes = 38 + 13 - 6 = 45
5. Calculate the Probability:
- Probability = Total favorable outcomes / Total tables
- Probability = 45/60
6. Express the Probability as a Fraction:
- Simplified, this probability is [tex]\(\frac{45}{60} = \frac{3}{4}\)[/tex].
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{3}{4}\)[/tex] or in terms of the choices provided, this corresponds to option B: [tex]\(\frac{45}{60}\)[/tex].
