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GATE CSE 2021 Set 2 Q39: Best order to attempt two questions for maximum expected marks

Question

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.

questionprobability of answering correctlymarks
QuesA0.810
QuesB0.520

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)?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
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Answer: D (official GATE 2021 final answer key)

Concept used: Expected value of a sequential process: the second question counts only if the first is correct.

First step: A first: 0.8 (10+0.5×20)0.8\,(10 + 0.5 \times 20). B first: 0.5 (20+0.8×10)0.5\,(20 + 0.8 \times 10). Compare.

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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