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: .