This can be analysed using probabilities. Sometimes the marking criteria requires states, in which case, you lose the mark either if you leave off states, or if you get state(s) wrong. Other times, the marking criteria does NOT require states, in which case you get the marks even if you put in no states, but I'm not sure if you lose marks if you put wrong states and states aren't required (don't think you do). The problem is, they don't tell you if they're marking for states for a given question.
Let's say you're
X% sure you've got the states right, and that there's a
Y% chance that they're marking for states. i.e. the probability that the states you think go in the equation are correct is
, say. So the probability you've got at least one state wrong is
. The probability that they're marking for states is
, say, so the probability that they're not marking for states is
.
So, there's four possibilities: you guess the states with the ones you think are right OR leave off states, AND states are being marked OR states aren't being marked.
So, if you do go with your guess for states, and the mark for getting the equation right according to the criteria is 1, and mark for wrong equation is 0, your expected mark is:
E
guess = P(guess is right)×(mark for correct answer) + P(guess is wrong)×P(states are being marked)×(mark for wrong answer) + P(guess is wrong)×P(states not being marked)×(mark for correct answer)
i.e.
.
Your expected mark if you decide not to guess states is
E
no guess = P(states not being marked)×(mark for correct answer) + P(states are being marked)×(mark for wrong answer)
Expanding and rearranging the formula for E
guess,
for any p
1 > 0 and q
2 ≠ 1.
So what we've shown is that if it's not certain that states are not going to be marked (i.e. q
2 ≠ 1),
you should always guess.
So, if you're unsure, always guess, unless you're told that states aren't required (in which case it's obvious you shouldn't guess).
Note. This was done assuming that, when states aren't required, incorrect states don't lose you marks. The calculations change if incorrect states still lose you marks even if states aren't required.