The exam in a course consists of 25 true/false questions, each worth two points, 35 multiple-choice questions, each worth one point, and 5 fill-in-the-blank questions, each worth three points. The probability that a student answers a true/false question correctly is 0.8, the probability that they answer a multiple-choice question correctly is 0.75, and the probability that they answer a fill-in-the-blank question correctly is 0.65. What is the expected score on the exam? Now consider the case where an incorrect answer on a true/false question results in a penalty of −1 point. 2 What is the resulting expected score?

Expected Score (No Negative Marking) = 135 points

Expected Score (with penalty) = 130 points

Step-by-step explanation:

First we find no. of true false answered correctly:

True/False Correct = (Total No. of True/False)(Probability to correctly answer true/false)

True/False Correct = (25)(0.8)

True/False Correct = 20

Now, for points scored from true/false:

True/False Score = (True/False Correct)(Points for 1 True/False)

True/False Score = (20)(2)

True/False Score = 40 points

Now, we find no. of mcqs answered correctly:

MCQs Correct = (Total No. of MCQs)(Probability to correctly answer MCQs)

MCQs Correct = (35)(0.75)

MCQs Correct = 26.25 = 26

Now, for points scored from MCQs:

MCQ Score = (MCQs Correct)(Points for 1 MCQ)

MCQ Score = (26)(1)

MCQ Score = 26 points

Now, we find no. of fill in the blanks answered correctly:

Fill in the blanks Correct = (Total No. of Fill in the blanks)(Probability to correctly answer Fill in the blanks)

Fill in the blanks Correct = (35)(0.65)

True/False Correct = 22.75 = 23

Now, for points scored from true/false:

Fill in the blanks Score = (Fill in the blanks Correct)(Points for 1 Fill in the blanks)

Fill in the blanks Score = (23)(3)

Fill in the blanks Score = 69 points

So, the expected total score will be:

Expected Score = 40 points + 26 points + 69 points

Expected Score = 135 points

IN CASE OF PENALTY:

We know that:

Incorrect True/Flase = Total True/False - Correct True/False = 25 - 20 = 5

Therefore,

Total Penalty = (Incorrect True/False)(Penalty on one)

Total Penalty = (5)(- 1 points)

Total Penalty = - 5 points

Now, expected score will be;

Expected Score (with penalty) = 135 points - 5 points

Expected Score (with penalty) = 130 points

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