7. In a multiple-choice test, each question has four options. Students will get 2 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? Show your calculations for expected value.

Question

amistre64 · Answer

expected value is determined as: gain x probability

amistre64 · Answer

if they answer they expected value is$$2\times\frac{1}{4}-1\times\frac{3}{4}$$
if they dont answer they expected value is just 0 i believe

tavia · Answer

ok could you explain how you got that

amistre64 · Answer

i thought i did ...

amistre64 · Answer

how many options do you get for a question?

tavia · Answer

4

amistre64 · Answer

good, and how many options are correct?

tavia · Answer

2

amistre64 · Answer

2 is the value of a correct option; how many correct options are there to a question?

tavia · Answer

1

amistre64 · Answer

then the probability of making  a correct guess is:  1/4
and the expected value is to gain 2 points

2 * 1/4

amistre64 · Answer

how many options are incorrect?

tavia · Answer

1

amistre64 · Answer

no, if you have 4 options, and only 1 is correct; how many does that leave to be incorrect?

tavia · Answer

3

amistre64 · Answer

then the probability of guess incorrectly is:  3/4
and the gain for each incorrect options is:  -1

the expected value of an incorrect guess is then:  -1*3/4

amistre64 · Answer

the expected value of the whole question is the sum of both of these

amistre64 · Answer

$$2\times \frac14-1\times \frac34=-\frac14$$

2-1-1-1 = -1, out of 4 options

amistre64 · Answer

since they "expect" to lose 1 point by guessing, and 0 points by leaving it blank; should they try to guess at it?

tavia · Answer

no

amistre64 · Answer

so is guessing advantageous?  or disadvantageuos?

tavia · Answer

disadvantageous

amistre64 · Answer

correct

tavia · Answer

thanks