QuestionA multiple-choice exam contains questions that each have 4 answer choices. One point is awarded for each correct answer, and 0.25 points are deducted for each incorrect answer. If an answer is left blank, then points are not awarded or deducted. Round the expected value to the nearest hundreth. a. What is the expected value if a student guesses on a question? b. Is it advantageous to guess if an answer is unknown? ? V c. What is the expected value if 0.5 points are deducted for each incorrect answer?
Studdy Solution
STEP 1
1. Each question has 4 answer choices.
2. The probability of guessing correctly is .
3. The probability of guessing incorrectly is .
4. Correct answers yield 1 point.
5. Incorrect answers result in a deduction of 0.25 points (for part a and b) and 0.5 points (for part c).
6. Blank answers yield 0 points.
STEP 2
1. Calculate the expected value for a guessed answer with a 0.25 point deduction.
2. Determine if guessing is advantageous.
3. Calculate the expected value for a guessed answer with a 0.5 point deduction.
STEP 3
Calculate the expected value for a guessed answer with a 0.25 point deduction:
The expected value is calculated as follows:
STEP 4
Determine if guessing is advantageous:
Since the expected value is positive, it is advantageous to guess if an answer is unknown.
STEP 5
Calculate the expected value for a guessed answer with a 0.5 point deduction:
The expected value is calculated as follows:
The expected values are:
a.
b. It is advantageous to guess if an answer is unknown.
c.
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