Questions: A multiple-choice exam has five possible answers for each question. For each correct answer, you are awarded 5 points. For each incorrect answer, 1 point is subtracted from your score. For answers left blank, no points are added or subtracted. a) If you do not know the correct answer to a particular question, is it to your advantage to guess? Explain. b) If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Explain. a) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Yes, it is to your advantage to guess because the expectation is . (Simplify your answer.) B. No, it is a disadvantage to guess because the expectation is . (Simplify your answer.) C. No, it is neither an advantage nor disadvantage to guess because the expectation is 0. b) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Yes, it is to your advantage to guess because the expectation is . (Simplify your answer.) B. No, it is a disadvantage to guess because the expectation is . (Simplify your answer.) C. No, it is neither an advantage nor disadvantage to guess because the expectation is 0.

A multiple-choice exam has five possible answers for each question. For each correct answer, you are awarded 5 points. For each incorrect answer, 1 point is subtracted from your score. For answers left blank, no points are added or subtracted.

a) If you do not know the correct answer to a particular question, is it to your advantage to guess? Explain.

b) If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Explain.

a) Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. Yes, it is to your advantage to guess because the expectation is .

(Simplify your answer.)

B. No, it is a disadvantage to guess because the expectation is .

(Simplify your answer.)

C. No, it is neither an advantage nor disadvantage to guess because the expectation is 0.

b) Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. Yes, it is to your advantage to guess because the expectation is .

(Simplify your answer.)

B. No, it is a disadvantage to guess because the expectation is .

(Simplify your answer.)

C. No, it is neither an advantage nor disadvantage to guess because the expectation is 0.
Transcript text: A multiple-choice exam has five possible answers for each question. For each correct answer, you are awarded 5 points. For each incorrect answer, 1 point is subtracted from your score For answers left blank, no points are added or subtracted a) If you do not know the correct answer to a particular question, is it to your advantage to guess? Explain. b) If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Explain. a) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Yes, it is to your advantage to guess because the expectation is $\square$ (Simplify your answer.) B. No, it is a disadvantage to guess because the expectation is $\square$ (Simplify your answer.) C. No, it is neither an advantage nor disadvantage to guess because the expectation is 0 . b) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Yes, it is to your advantage to guess because the expectation is $\square$ ]. (Simplify your answer.) B. No, it is a disadvantage to guess because the expectation is $\square$ . (Simplify your answer.) C. No, it is neither an advantage nor disadvantage to guess because the expectation is 0 .
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Solution

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Solution Steps

Step 1: Calculate the Expected Value (EV) of Guessing

To calculate the expected value of guessing, we use the formula: \[ EV = \frac{p}{n-k} - \frac{q \cdot (n-k-1)}{n-k} \] Where,

  • \(p = 5\) points are awarded for each correct answer,
  • \(q = 1\) points are subtracted for each incorrect answer,
  • \(n = 5\) is the total number of possible answers, and
  • \(k = 0\) is the number of choices the examinee can eliminate as incorrect. Substituting the given values into the formula, we get: \[ EV = \frac{5}{5-0} - \frac{1 \cdot (5-0-1)}{5-0} = 0.2 \]
Step 2: Decision Criteria

Since \(EV > 0\), it is to the examinee's advantage to guess. The expected value of guessing is positive, indicating an average gain in points.

Final Answer:

Given the parameters (n=5, p=5, q=1, k=0), it is advantageous to guess as the expected value is 0.2.

Step 1: Calculate the Expected Value (EV) of Guessing

To calculate the expected value of guessing, we use the formula: \[ EV = \frac{p}{n-k} - \frac{q \cdot (n-k-1)}{n-k} \] Where,

  • \(p = 5\) points are awarded for each correct answer,
  • \(q = 1\) points are subtracted for each incorrect answer,
  • \(n = 5\) is the total number of possible answers, and
  • \(k = 1\) is the number of choices the examinee can eliminate as incorrect. Substituting the given values into the formula, we get: \[ EV = \frac{5}{5-1} - \frac{1 \cdot (5-1-1)}{5-1} = 0.5 \]
Step 2: Decision Criteria

Since \(EV > 0\), it is to the examinee's advantage to guess. The expected value of guessing is positive, indicating an average gain in points.

Final Answer:

Given the parameters (n=5, p=5, q=1, k=1), it is advantageous to guess as the expected value is 0.5.

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