Questions: Mrs. Burke's mathematics class has 102 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collect yesterday's work. Mrs. Burke's Mathematics Class Academic Year Mathematics Majors Non-Mathematics Majors ------------- ------------------ ---------------------- Freshmen 14 16 Sophomores 13 11 Juniors 17 9 Seniors 10 12 Step 1 of 2: What is the probability that she selects a mathematics major, given that she chooses randomly from only the sophomores? Enter a fraction or round your answer to 4 decimal places, if necessary.

Mrs. Burke's mathematics class has 102 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collect yesterday's work. Mrs. Burke's Mathematics Class Academic Year Mathematics Majors Non-Mathematics Majors ------------- ------------------ ---------------------- Freshmen 14 16 Sophomores 13 11 Juniors 17 9 Seniors 10 12 Step 1 of 2: What is the probability that she selects a mathematics major, given that she chooses randomly from only the sophomores? Enter a fraction or round your answer to 4 decimal places, if necessary.
Transcript text: Mrs. Burke's mathematics class has 102 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collect yesterday's work. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Mrs. Burke's Mathematics Class } \\ \hline Academic Year & Mathematics Majors & Non-Mathematics Majors \\ \hline Freshmen & 14 & 16 \\ \hline Sophomores & 13 & 11 \\ \hline Juniors & 17 & 9 \\ \hline Seniors & 10 & 12 \\ \hline \end{tabular} Step 1 of 2: What is the probability that she selects a mathematics major, given that she chooses randomly from only the sophomores? Enter a fraction or round your answer to 4 decimal places, if necessary. Answer Tables Keypad
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Solution

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Solution Steps

Step 1: Calculate the probability of selecting a student with the specific characteristic from the entire class

$$P(A) = \frac{n_A}{N} = \frac{13}{24} = 0.542$$

Step 2: Calculate the probability of selecting a student from the subset

$$P(B) = \frac{n_B}{N} = \frac{24}{24} = 1$$

Step 3: Calculate the probability of selecting a student who belongs to both the subset and has the specific characteristic

$$P(A \cap B) = \frac{n_{A \cap B}}{N} = \frac{13}{24} = 0.542$$

Step 4: Calculate the conditional probability of selecting a student with the specific characteristic given that the student is from the subset

$$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.542}{1} = 0.542$$

Final Answer:

The conditional probability of selecting a student with the specific characteristic given that the student is from the subset is 0.542.

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