SOLUTION: Students will get 3 points for each correct answer; lose 1 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answ

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Question 470895: Students will get 3 points for each correct answer; lose 1 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer?
can someone walk me through this please
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Students will get 3 points for each correct answer; lose 1 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer?
This is an expectation problem:

The problem does not specify how many choices there are for the answer
to the question. So I will suppose there are n choices for the answer.
Then the probability of guessing correctly is 1%2Fn and the 
probability of guessing incorrectly is 1 - 1%2Fn.

Possibility              x (points)    P(x)     Expectation = x*P(x)
 
Answering correctly          3         1/n           3/n
Answering incorrectly       -1        1-1/n        -1(1-1/n)

So the total expectation on guessing is

3%2Fn-1%281-1%2Fn%29
3%2Fn-1%2B1%2Fn
4%2Fn-1

Since 0 points are gotten if the problem is left blank, we
want to know how many choices n must be in order for the
expection to be greater than 0.  So we set that > 0

4%2Fn-1%3E0

Multiply through by n

4-n%3E0

4%3En

So if there are less than 4 choices for the answer to each question,
it is to the student's advantage to guess.  If there are exactly 4
choices per question, then the expectation will be 0 either way.
However if there are more than 4 choices for each question, it is
better to leave the question unanswered.

Edwin