To solve the question "Assuming a student is taking a foreign language, what is the probability the student is also in high school?", we need to analyze and interpret the probabilities provided in the given table.
The table provided, Table B, gives us the probabilities of being in middle school or high school, given whether or not a student is taking a foreign language.
Here is a step-by-step approach to solving the problem:
1. Identify Available Probabilities:
- The table provides the conditional probability of students being in middle school given that they are taking a foreign language, [tex]\( P(\text{Middle School} | \text{Taking a Foreign Language}) = 0.68 \)[/tex].
- Similarly, it provides the conditional probability of students being in high school given that they are taking a foreign language, [tex]\( P(\text{High School} | \text{Taking a Foreign Language}) = 0.88 \)[/tex].
2. Determine the Relevant Probability:
- The problem asks for the probability that a student is in high school given that they are taking a foreign language. This is exactly [tex]\( P(\text{High School} | \text{Taking a Foreign Language}) \)[/tex].
3. Read the Probability from the Table:
- From Table B, we find that [tex]\( P(\text{High School} | \text{Taking a Foreign Language}) = 0.88 \)[/tex].
Thus, the probability that a student is in high school given that they are taking a foreign language is 0.88.
