Question

A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Ten points are awarded for each correct answer, but the student loses 2 points for an incorrect answer. Questions left blank neither receive nor lose points. What is the minimum number of options that the student should be able to rule out before making a guess on any particular question?

Answer 1

The Choices Are CHOOSE ONE
A Three
B None
C Two
D One

Answer 2

assuming that the student knows nothing and guesses, the probability she is right is one in five, or \(\frac{1}{5}\) and the chances she is wrong is \(\frac{4}{5}\)
gets \(+10\) for guessing right, \(-2\) for guessing wrong
\[\frac{1\times 10-4\times 2}{5}=\frac{10-8}{5}=\frac{2}{5}\] and since this is a positive number, it is good to guess no matter what

Answer 3

you can also think of it this way.
suppose there are ten questions on the test, the student guesses at all of them. in all likelihood she will get 2 out of the ten right for 20 points and miss 8 out of the ten and be deducted 16 points. but since \(20-16=4\) she will still score 4 point without knowing anything at all!

Answer 4

But than How come 4 it's not on the choices I have ?

Answer 5

oh because the question asked

What is the minimum number of options that the student should be able to rule out before making a guess on any particular question?

and since you will get a positive score just by guessing, you do not need to rule out any
none is the answer

Answer 6

i think my answer was not clear. i computed what she expected to get just by guessing without ruling any question out, and that was a positive number

Answer 7

Oh Okey I got it now
I m sorry To bother and thank you for the help

Answer 8

but suppose for example that there were 3 points deducted. then guessing one out of 5 is not a good policy, because
\[10\times \frac{1}{5}-3\frac{4}{5}=\frac{10-12}{5}=-\frac{2}{5}\] so that would be a net loss
in that case you would have to rule out one question and increase your chances to one out of four instead of one out of five

Answer 9

it is no bother
hope it is clearer