<p>Say ETS gives you 5 answer choices to a multiple-choice question of the SAT. You clearly have no idea how to answer this question, but you pick one. ETS then eliminates three answer choices for you and you're now down to your answer and one other. Is it in your best interest to switch your choice or remain with the same one for the correct answer?</p>
<p>This sounds very similar to the Monty Hall problem. If and only if you know that the three answer choices ETS eliminates for you are all wrong, then it would be in your best interest to switch. This is because when you first pick, you have a 20% of getting the right answer. That means if you picked all 4 of the other choices, you would have an 80% choice of getting the right answer (basically [A] = 20 and [B,C,D,E] = 80). If ETS eliminates B, C, and D because they are guaranteed to be the right answer, then that means [A] = 20 and [E] = 80 because E is the last remaining member of the second group. The Monty Hall problem usually does this with three choices and eliminates one wrong answer that was not picked, but the effect is more pronounced the more choices you have (try 100). Remember, this only works because ETS knows which choices are wrong and the ones that have been gotten rid of are wrong. If that process is random, then it’s truly a 50/50 shot.</p>
<p>Wasnt there something like this in the move 21?</p>
<p>Okay, would this work similarly for yourself? Pick an answer first and if you worked your way to knowing three which were wrong, you should switch (assuming your answer you picked wasn’t marked off)?</p>
<p>You should ALWAYS switch. Statistically, you’ll be right 3/5’s of the time.</p>
<p>OK, in THEORY, if you truly guessed at random, and only after that then found that you could eliminate (correctly – which is no sure thing) 3 of the 4 that you did not pick, then yes, though it seems odd, it would be better to switch. If you google “monty hall paradox” you will find a ton of info about this including web sites with applets where you can simulate playing the game and see what happens with many trials so that you can convince yourself that the switching plan is in fact better.</p>
<p>BUT BACK TO REALITY: if this is the kind of thing you think about during the test, you are nuts! Your first guess was probably not truly random and you MAY have accidentally ruled out the right answer. But if you are confident that you correctly ruled out three wrong answers, then you are not clueless – you obviously have some correct mathematical insight about this problem. Now use your best JUDGEMENT and pick from the remaining answers. Don’t look for gimmicks like “always go with your first instinct”, “never go with your first instinct”, “always pick b”, “pick which ever letter you’ve used least”-- that’s all voodoo nonsense. Just use your judgement. It won’t always be right but it will always be the best bet.</p>