E-StoreWhy you should guess -- the mathematics behind guessing answers in objective examinations
13 May 2007 00:34:42 IST
Why you should guess -- the mathematics behind guessing answers in objective examinations
Many times I've seen people saying that because of negative marking, one should only attempt questions in objective examinations that one is fully sure of.
I've seen this advice being given for the IIT-JEE, the AIEEE, and even the UPSC exams (negative marking has been introduced this year).
This advice is WRONG, WRONG, WRONG.
Why am I saying so? It's all a question of probabilities. Read on to find out.
Why are negative marks given?
Before negative marking was introduced, several students got through just by guessing questions blindly.
Negative marking is meant to discourage blind guessing.
The keyword is BLIND.
Negative marking is NOT meant to discourage intelligent guessing.
Let's take the example of the IIT-JEE/AIEEE straight (one option correct out of four) questions (+3/-1). Say, there are 60 questions. You do not know the answers to any of them.
1. Guess blindly
Since one out of four options is correct, odds are, you'll get one out of every four questions correct.
That means that you should get around 15 questions correct, and 45 incorrect. So your total will be around (15 × 3 - 45 × 1) = 0, rendering you almost equal to a person who left the paper blank.
This is how negative marking discourages blind guessing.
2. Eliminate 1 option in every question
Let's say you know enough to eliminate one option in every question. Therefore, you have to guess among 3 answers. So the odds are that you get 1 out of every 3 answers correct.
This means that you should get around 20 answers correct, and 40 wrong. The total will be around (20 × 3 - 40 × 1) = 20. This means that you will be better off than if you had left the paper blank.
3. Eliminate 2 options in every question
Your odds will improve further. You should get around 30 answers correct, and 30 wrong. The total will be around (30 × 3 - 30 × 1) = 60. Your score is MUCH better than if you had left the paper blank.
Moral of the story
For a +3/-1 question, ALWAYS guess once you have eliminated at least one answer. ALWAYS.
Note that this is valid for all multiple choice questions in which the negative mark for a wrong answer is 1/(n-1) times the mark for a right answer. n is the number of options.
The situation can change according to the value of the fraction.
For the +4/-1 comprehension questions (in this year's IIT-JEE):
Even if you guess blindly, in 60 questions your score will be around (15 × 4 - 45 × 1) = 15. Therefore you should ALWAYS attempt such questions, even if you have to guess blindly.
For the +5/-1 multiple answer questions (previous IIT-JEEs):
There are 14 possible incorrect answers and only one possible correct answer. In 60 questions, if you guess blindly, you will get (4 × 5 - 56 × 1) = -36, i.e. badly hit.
If you are sure of one option being correct, there can be 8 possible answers -- you will get 1 out of 8 answers right. The odds are still against you.
If you are sure of 1 correct option and one other option (correct or incorrect), there can be 4 possible answers. The odds are *now* in your favour.
If you are sure of one option being incorrect, there can be 7 possible answers -- the odds are against you.
If you know two options are incorrect, there can be 3 possible answers -- the odds are in your favour.
Therefore, guessing is a bad idea, unless you are sure of two options either way.
Remember -- this is not a substitute for knowing the answers. You will always score the highest if you know the answers.
PS. It is possible that by chance you get all the answers you guessed right, or all the answers you guessed wrong. This chance is very small, however. To get all 60 questions wrong, the chances are (3/4)60 = 3.19 × 10-8. The probability of getting all 60 questions correct is even lower: (1/4)60 = 7.52 × 10-37.
EDIT: Some more information on this can be found at http://en.wikipedia.org/wiki/Expected_value . The concept of expected values is also present in gambling, and guessing is quite similar to gambling, in a mathematical sense. The important thing is to get the odds in your favour.
Comments (19)
Siddharth Agarwal
Hot goIITian
Joined: 9 Apr 2007 20:25:33 IST
Posts: 166
13 May 2007 00:42:04 IST
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Do rate me if you find this useful.
13 May 2007 01:28:50 IST
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nice study...!!!!! But I had tried intelligent guessing method in my institute test's and I faired badly... But now I attempt only of which I am 101% sure..!!!! and I performing far better...!! however, it depands upon person to person which method to adopt...
13 May 2007 01:43:31 IST
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Chirag, then you were just unlucky. The maths is quite solid. I made a few guesses in my IIT-JEE paper and I got just what the maths predicts. The chances of getting X answers correct are determined by a Bernoulli distribution.
13 May 2007 15:30:04 IST
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merci...ive been trying to impress this upon my friends 4 a looong time now...well compiled...
13 May 2007 16:06:42 IST
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I agree, but in the end it's all luck. On good day all of ur guesses r rt and on a bad day most are wrong. But still we should do guessing.
13 May 2007 16:19:54 IST
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The concept is similar to that in gambling. On a good day you will win a lot of money, and on a bad day you will lose a lot. You cannot control that. All you can do is make sure that your odds are favourable.
All I have done is enumerated when the odds are favourable and when they are not.
All I have done is enumerated when the odds are favourable and when they are not.
14 May 2007 04:46:58 IST
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R U SURE OF THIS
HAVE U TRIED IT
THANKS FOR THE POST
HAVE U TRIED IT
THANKS FOR THE POST
14 May 2007 13:42:19 IST
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"R U SURE OF THIS"
Yes, and you can be too, if you take the time to read and understand the mathematics.
Yes, and you can be too, if you take the time to read and understand the mathematics.
11 Jun 2007 23:02:21 IST
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the science of guessing. gud only if it works in jee
12 Jun 2007 18:52:36 IST
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good work but one cant put at stakes ones career on bloody guesses
this method works only when u know very less of the paper...
this method works only when u know very less of the paper...
13 Jun 2007 20:01:05 IST
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Gr8 work man , but that doesn't always work as planned.In fact when
you have to pick one out of three , you have 75% chance of choosing the correct one out . But if you have to pick one out of 2, then there is 25% probablity of choosing the correct one.Its due to our human instinct that our brain calcultes the probabilty as 50-50 each.Besides , the heart factor is also there.Remember
"Every mystery can be solved using Mathematics".
-MR. IITIAN
you have to pick one out of three , you have 75% chance of choosing the correct one out . But if you have to pick one out of 2, then there is 25% probablity of choosing the correct one.Its due to our human instinct that our brain calcultes the probabilty as 50-50 each.Besides , the heart factor is also there.Remember
"Every mystery can be solved using Mathematics".
-MR. IITIAN
14 Jun 2007 09:34:41 IST
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@sanky: In fact, it works the best when you know most of the paper and there are a few questions to be guessed. Great chance of fetching bonus points :)
@Mr.IITIAN: I don't get you. Could you please elaborate in my nudgebook?
@Mr.IITIAN: I don't get you. Could you please elaborate in my nudgebook?
14 Jun 2007 10:46:17 IST
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cool! but you know what it's not always so good ....
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