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!
Answer :
- Define events: A (round table), B (table by the window).
- Use inclusion-exclusion principle: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
- Calculate probabilities: $P(A) = \frac{38}{60}$, $P(B) = \frac{13}{60}$, $P(A \cap B) = \frac{6}{60}$.
- Find the final probability: $P(A \cup B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} = \boxed{\frac{45}{60}}$.
### Explanation
1. Understanding the Problem
Let's break down this probability problem step by step! We need to find the probability that a customer will be seated at a round table or a table by the window. To do this, we'll use the principle of inclusion-exclusion.
2. Defining Events
Let A be the event that a table is round, and B be the event that a table is by the window. We want to find $P(A \cup B)$, which means the probability of A or B happening.
3. Applying the Inclusion-Exclusion Principle
The formula for $P(A \cup B)$ is: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ This formula helps us avoid counting the tables that are both round and by the window twice.
4. Calculating Individual Probabilities
Now, let's calculate each probability:
$P(A)$ (probability of a round table) = $\frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60}$
$P(B)$ (probability of a table by the window) = $\frac{\text{Number of tables by the window}}{\text{Total number of tables}} = \frac{13}{60}$
$P(A \cap B)$ (probability of a round table by the window) = $\frac{\text{Number of round tables by the window}}{\text{Total number of tables}} = \frac{6}{60}$
5. Combining the Probabilities
Plug these values into the formula: $$P(A \cup B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}$$
6. Simplifying the Result
Now, let's simplify: $$P(A \cup B) = \frac{38 + 13 - 6}{60} = \frac{45}{60}$$
7. Final Answer
So, the probability that a customer will be seated at a round table or by the window is $\frac{45}{60}$.
### Examples
This type of probability calculation is useful in many real-world scenarios, such as planning events or managing resources. For example, a party planner might use this to determine the likelihood that a guest will want either a vegetarian or gluten-free meal, ensuring they have enough options available. Similarly, a store manager could use it to predict how many customers will be interested in a product that is both on sale and eco-friendly, helping them optimize their marketing strategy.
- Use inclusion-exclusion principle: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
- Calculate probabilities: $P(A) = \frac{38}{60}$, $P(B) = \frac{13}{60}$, $P(A \cap B) = \frac{6}{60}$.
- Find the final probability: $P(A \cup B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} = \boxed{\frac{45}{60}}$.
### Explanation
1. Understanding the Problem
Let's break down this probability problem step by step! We need to find the probability that a customer will be seated at a round table or a table by the window. To do this, we'll use the principle of inclusion-exclusion.
2. Defining Events
Let A be the event that a table is round, and B be the event that a table is by the window. We want to find $P(A \cup B)$, which means the probability of A or B happening.
3. Applying the Inclusion-Exclusion Principle
The formula for $P(A \cup B)$ is: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ This formula helps us avoid counting the tables that are both round and by the window twice.
4. Calculating Individual Probabilities
Now, let's calculate each probability:
$P(A)$ (probability of a round table) = $\frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60}$
$P(B)$ (probability of a table by the window) = $\frac{\text{Number of tables by the window}}{\text{Total number of tables}} = \frac{13}{60}$
$P(A \cap B)$ (probability of a round table by the window) = $\frac{\text{Number of round tables by the window}}{\text{Total number of tables}} = \frac{6}{60}$
5. Combining the Probabilities
Plug these values into the formula: $$P(A \cup B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}$$
6. Simplifying the Result
Now, let's simplify: $$P(A \cup B) = \frac{38 + 13 - 6}{60} = \frac{45}{60}$$
7. Final Answer
So, the probability that a customer will be seated at a round table or by the window is $\frac{45}{60}$.
### Examples
This type of probability calculation is useful in many real-world scenarios, such as planning events or managing resources. For example, a party planner might use this to determine the likelihood that a guest will want either a vegetarian or gluten-free meal, ensuring they have enough options available. Similarly, a store manager could use it to predict how many customers will be interested in a product that is both on sale and eco-friendly, helping them optimize their marketing strategy.
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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
