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
failed

Solution

failed
failed

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.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
An inadequate flow of blood is lymphangiography hematology hypoperfusion perfusion
failedAnswered
¿Cuál de las siguientes gráficas representa cantidades que varían directamente proporcional?
failedAnswered
(b) Subtract. 1-P(x) = 3/8 (c) Select the answer that makes the sentence true.
failedAnswered
What is her deadline for paying no interest in a leap year? A. March 27 B. March 30 C. March 29 D. March 28 Is the finance company likely to use exact or ordinary interest and why? A. Money lenders typically use exact interest (365 days per year vs. 360 days per year) for loans to require slightly lower interest. B. Money lenders typically use ordinary interest (360 days per year vs. 365 days per year) for loans to require slightly higher interest. C. Money lenders typically use ordinary interest (360 days per year vs. 365 days per year) for loans to require slightly lower interest. D. Money lenders typically use exact interest (365 days per year vs. 360 days per year) for loans to require slightly higher interest. 3. If Jillian takes the 90 days same as cash and pays within 90 days, what is her payoff amount? square square (Round to the nearest cent as needed.)
failedAnswered
Find the sum of the infinite geometric sequence 450, 180, 72, 28.8, 11.52 ... Sum =