GATE CS 2021 Set 2 — Question 39
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Engineering Mathematics → Probability & Statistics → Expectation & Variance
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Question
In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.
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)?
- 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.
| question | probability of answering correctly | marks |
|---|---|---|
| QuesA | 0.8 | 10 |
| QuesB | 0.5 | 20 |
Correct answer
(D) First QuesA and then QuesB. Expected marks 16.
Solution
Let
Let
The expected marks for an order (First , then ) is given by:
Case 1: Order QuesA then QuesB
Here, and .
Case 2: Order QuesB then QuesA
Here, and .
Comparing the expected marks, .
Thus, the student should attempt QuesA first and then QuesB to maximize expected marks, which is 16.
P(A) and M(A) be the probability of answering QuesA correctly and its marks, respectively.Let
P(B) and M(B) be the probability of answering QuesB correctly and its marks, respectively.The expected marks for an order (First , then ) is given by:
Case 1: Order QuesA then QuesB
Here, and .
Case 2: Order QuesB then QuesA
Here, and .
Comparing the expected marks, .
Thus, the student should attempt QuesA first and then QuesB to maximize expected marks, which is 16.
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