Thread: A test consists of 5 questions ....

Hi All,

A probability problem, not sure whether this is a combination problem or permutation.

A test consists of 5 questions. A correct answer scores 2 marks and an incorrect one, to penalize guessing, scores -1. Assuming that all the questions are answered, find probability of scoring -2.

I figured that only way to score -2 is 1 correct and 4 incorrect, 2 - 4 = -4. All other combinations are incorrect.
Stuck here, Can you guys give me a hint on how to proceed further? Thanks!

Hello, mathguy80!

A test consists of 5 questions.
A correct answer scores 2 marks and an incorrect one scores -1.
Assuming that all the questions are answered, find probability of scoring -2.

I figured that only way to score -2 is 1 correct and 4 incorrect: (1)(2) + 4(-1) = -2
. . Right!
Can you guys give me a hint on how to proceed further?

I assume that the student is randomly guessing the answers,
. . and that the probability of guessing a correct answer is

To get a score of -2, he must get one Correct and four Incorrect, in some order.


There are 5 choices for the Correct answer.
The probability that answer being correct is

He must get the other four equations Incorrect.
The probability of this is:


Therefore: .

Originally Posted by mathguy80

A test consists of 5 questions. A correct answer scores 2 marks and an incorrect one, to penalize guessing, scores -1. Assuming that all the questions are answered, find probability of scoring -2.
I figured that only way to score -2 is 1 correct and 4 incorrect, 2 - 4 = -4.

There are several difficulties with the statement of this question.
It says nothing about the probability of guessing the correct answer to a given question. So let us say that is the probability that any given question is answered correctly.
Then the probability of getting exactly one correct is .

Thanks @Soroban. Your answer 5/32 checks out. I hadn't made the connection that probability of guessing a correct answer is 1/2.

@Plato, Thanks as well. This is probably an advanced idea, but allowing for variable probability of answering question correctly is very cool. Will keep this in mind for future study.