College

We appreciate your visit to Select the correct answer A restaurant has a total of 60 tables Of those tables 38 are round and 13 are located by the window. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Select the correct answer.

A restaurant has a total of 60 tables. Of those tables, 38 are round and 13 are located by the window. There are 6 round tables by the window.

If tables are randomly assigned to customers, what is the probability that a customer will be seated at a round table or by the window?

A. [tex]\frac{45}{60}[/tex]
B. [tex]\frac{29}{60}[/tex]
C. [tex]\frac{41}{60}[/tex]
D. [tex]\frac{47}{60}[/tex]

Answer :

To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we can use the formula for the probability of the union of two events.

Let's break this down step-by-step:

1. Identify the Events:
- Event A: A table is round.
- Event B: A table is by the window.

2. Given Values:
- Total tables = 60
- Round tables = 38
- Tables by the window = 13
- Round tables by the window = 6

3. Apply the Formula:
- The probability of the union of two events (A or B) is given by:

[tex]\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\][/tex]

- [tex]\( P(A) \)[/tex] is the probability of a round table, which is the number of round tables divided by total tables. So:

[tex]\[
P(A) = \frac{38}{60}
\][/tex]

- [tex]\( P(B) \)[/tex] is the probability of a table by the window, which is the number of window tables divided by total tables. So:

[tex]\[
P(B) = \frac{13}{60}
\][/tex]

- [tex]\( P(A \text{ and } B) \)[/tex] is the probability of both round and by the window, which is the number of round tables by the window divided by total tables. So:

[tex]\[
P(A \text{ and } B) = \frac{6}{60}
\][/tex]

4. Calculate the Probability:

- Substituting these values into the formula:

[tex]\[
P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}
\][/tex]

- This simplifies to:

[tex]\[
P(A \text{ or } B) = \frac{45}{60} = 0.75
\][/tex]

5. Convert to a Fraction:

- The probability expressed as a fraction from the total number of tables is:

[tex]\[
P(A \text{ or } B) = \frac{45}{60}
\][/tex]

Given these steps, the correct answer is option A: [tex]\(\frac{45}{60}\)[/tex].

Thanks for taking the time to read Select the correct answer A restaurant has a total of 60 tables Of those tables 38 are round and 13 are located by the window. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada