Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Table B: Frequency of Foreign-Language Studies by Row

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & \begin{tabular}{c}
Taking a \\
Foreign \\
Language
\end{tabular} & \begin{tabular}{c}
Not Taking a \\
Foreign \\
Language
\end{tabular} & Total \\
\hline
\begin{tabular}{c}
Middle \\
School
\end{tabular} & 0.68 & 0.32 & 1.0 \\
\hline
High School & 0.88 & 0.12 & 1.0 \\
\hline
Total & 0.8 & 0.2 & 1.0 \\
\hline
\end{tabular}

Which table could be used to answer the question "Assuming a student is taking a foreign language, what is the probability the student is also in high school?"

A. Table A, because the given condition is that the student is in high school.
B. Table [tex]$A$[/tex], because the given condition is that the student is taking a foreign language.
C. Table B, because the given condition is that the student is in high school.
D. Table [tex]$B$[/tex], because the given condition is that the student is taking a foreign language.

Sagot :

GinnyAnswer
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.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.