In an examination, a student can choose the order in which two questions…
2021
In an examination, a student can choose the order in which two questions (\(QuesA\) and \(QuesB\)) must be attempted.
- If the first question is answered wrong, the student gets zero marks.
- If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.
- If both the questions are answered correctly, the student gets the sum of the marks of the two questions.
The following table shows the probability of correctly answering a question and the marks of the question respectively.
\(\begin{array}{c|c|c} \text{question} & \text{probabilty of answering correctly} & \text{marks} \\ \hline \textsf{QuesA} & 0.8 & 10 \\ \textsf{QuesB} & 0.5 & 20 \end{array}\)
Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?
- A.
First
\(QuesA\)and then\(QuesB\). Expected marks 14 - B.
First
\(QuesB\)and then\(QuesA\). Expected marks 14 - C.
First
\(QuesB\)and then\(QuesA\). Expected marks 22 - D.
First
\(QuesA\)and then\(QuesB\). Expected marks 16
Attempted by 24 students.
Show answer & explanation
Correct answer: D
Key idea: compute the expected marks for each ordering and choose the ordering with the larger expected value.
Order: QuesA first, then QuesB. Expected = 0.8 × (10 + 0.5 × 20) = 0.8 × 20 = 16.
Order: QuesB first, then QuesA. Expected = 0.5 × (20 + 0.8 × 10) = 0.5 × 28 = 14.
Conclusion: Attempt QuesA first then QuesB because the expected marks are higher (16 > 14). The maximum expected marks achievable is 16.