Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To solve the problem "Assuming a student is taking a foreign language, what is the probability the student is also in high school?", let's break down the information step-by-step using the provided data.
Step 1: Understand the given table
We have data on students taking and not taking a foreign language in both middle school and high school.
Here’s the table for reference:
[tex]\[ \begin{array}{|c|c|c|c|} \hline & \text{Taking a Foreign Language} & \text{Not Taking a Foreign Language} & \text{Total} \\ \hline \text{Middle School} & 0.68 & 0.32 & 1.0 \\ \hline \text{High School} & 0.88 & 0.12 & 1.0 \\ \hline \text{Total} & 0.8 & 0.2 & 1.0 \\ \hline \end{array} \][/tex]
Step 2: Extract necessary probabilities
- The probability that a student is in high school and is taking a foreign language is 0.88 (from the High School row, Taking a Foreign Language column).
- The total probability that a student is taking a foreign language is 0.8 (from the Total row, Taking a Foreign Language column).
Step 3: Calculate the joint probability
To find the probability that a student is both in high school and taking a foreign language:
[tex]\[ P(\text{Taking a Foreign Language} \cap \text{High School}) = 0.88 \times 0.2 = 0.176 \][/tex]
Step 4: Calculate the desired conditional probability
We need to find [tex]\( P(\text{High School} \mid \text{Taking a Foreign Language}) \)[/tex]. The conditional probability formula is:
[tex]\[ P(\text{High School} \mid \text{Taking a Foreign Language}) = \frac{P(\text{Taking a Foreign Language} \cap \text{High School})}{P(\text{Taking a Foreign Language})} \][/tex]
Using the numbers we have:
[tex]\[ P(\text{High School} \mid \text{Taking a Foreign Language}) = \frac{0.176}{0.8} = 0.22 \][/tex]
Conclusion:
- Probability that a student is taking a foreign language and is in high school: 0.176
- Probability that a student is in high school given they are taking a foreign language: 0.22
Answering the specific question:
"Table [tex]\( B \)[/tex], because the given condition is that the student is taking a foreign language."
This is correct because Table [tex]\( B \)[/tex] presents the frequencies needed to determine conditional probabilities involving students taking foreign languages and being in high school or middle school.
Step 1: Understand the given table
We have data on students taking and not taking a foreign language in both middle school and high school.
Here’s the table for reference:
[tex]\[ \begin{array}{|c|c|c|c|} \hline & \text{Taking a Foreign Language} & \text{Not Taking a Foreign Language} & \text{Total} \\ \hline \text{Middle School} & 0.68 & 0.32 & 1.0 \\ \hline \text{High School} & 0.88 & 0.12 & 1.0 \\ \hline \text{Total} & 0.8 & 0.2 & 1.0 \\ \hline \end{array} \][/tex]
Step 2: Extract necessary probabilities
- The probability that a student is in high school and is taking a foreign language is 0.88 (from the High School row, Taking a Foreign Language column).
- The total probability that a student is taking a foreign language is 0.8 (from the Total row, Taking a Foreign Language column).
Step 3: Calculate the joint probability
To find the probability that a student is both in high school and taking a foreign language:
[tex]\[ P(\text{Taking a Foreign Language} \cap \text{High School}) = 0.88 \times 0.2 = 0.176 \][/tex]
Step 4: Calculate the desired conditional probability
We need to find [tex]\( P(\text{High School} \mid \text{Taking a Foreign Language}) \)[/tex]. The conditional probability formula is:
[tex]\[ P(\text{High School} \mid \text{Taking a Foreign Language}) = \frac{P(\text{Taking a Foreign Language} \cap \text{High School})}{P(\text{Taking a Foreign Language})} \][/tex]
Using the numbers we have:
[tex]\[ P(\text{High School} \mid \text{Taking a Foreign Language}) = \frac{0.176}{0.8} = 0.22 \][/tex]
Conclusion:
- Probability that a student is taking a foreign language and is in high school: 0.176
- Probability that a student is in high school given they are taking a foreign language: 0.22
Answering the specific question:
"Table [tex]\( B \)[/tex], because the given condition is that the student is taking a foreign language."
This is correct because Table [tex]\( B \)[/tex] presents the frequencies needed to determine conditional probabilities involving students taking foreign languages and being in high school or middle school.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
