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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.  question Probability of answering correctly marks QuesA 0.8 10 QuesB 0.5 20 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)? 

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.  question Probability of answering correctly marks QuesA 0.8 10 QuesB 0.5 20 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)?  Correct Answer First QuesA and then QuesB. Expected marks 16.

The correct answer is option 4

Explanation

First, we answer A, then B:
Expected marks = the probability that A is wrong × 0  + the probability that A is correct  ×  probability that B is wrong  × 10

                             + the probability that A is correct ×  probability that B is correct × 30
                             =0.2 × 0+0.8 × 0.5 × 10+0.8 × 0.5 × 30
                             =0+4+12
                             =16
If first, we answer B, then A:

Expected marks = the probability that B is wrong   × 0 + the probability that B is correct  ×  probability that A is wrong  × 10

                            + the probability that B is correct ×  probability that A is correct × 30

                           = 0.5 × 0+0.2 × 0.5 × 20+0.8 × 0.5 × 30
                           = 0+2+12
                           =14

So, the Correct answer is  First QuesA and then QuesB and  Expected marks 16.

Related Questions

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