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Probability

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Probability

by sud21 » Mon Sep 28, 2015 5:01 pm
On a test, students receive 3 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?

-2

-1

0

1

2
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by [email protected] » Mon Sep 28, 2015 7:42 pm
Hi sud21,

This question really isn't about probability. Since the prompt as asking for the minimum score possible under a specific series of conditions, we want to try to maximize the number of wrong answers (out of 6 questions).

For the correct answers, we have 5 Bs and 1C
For the submitted answers, we have 3Bs and 3Cs

First, let's take the 3 Cs and put them all on 3 'correct Bs' --> that's 3 wrong answers.
Next, let's take 1 B and put it on the 1 'correct C' --> that's 1 wrong answer.
That leaves the final 2 Bs on the final 2 'correct Bs' --> that's 2 CORRECT answers.

Under the scoring system, each correct answer is worth 3 points and each incorrect answer is -1 point.

2(3) + 4(-1) = +2

Final Answer: E

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Rich
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