Random guesses v the same answer every time

[jess1]

hello, i made this account just so i could figure this out--i realize people often do that (to make an account without an initial intention of becoming a regular), so i apologize for that; if you feel i am taking advantage of your time and expertise, then i understand. but i am not trying to figure this out for homework or for an upcoming test or anything like that. i just am really interested and don't have the knowledge to figure it out myself and i can't find a good explanation online.

so, of course i have heard that the best way to get the highest score (via guessing) is to just guess the same answer every time, as opposed to guessing randomly on every question, and that makes sense, but what i could not figure out was how to just prove it mathematically. i haven't taken stats :(

i figured the best way to look at it is to take 5 problems with 5 choices each and assume that each letter will be the correct answer 1 time. makes sense right? small sample size that is representative of an infinitely large one?

1) A B C D E
2) A B C D E
3) A B C D E
4) A B C D E
5) A B C D E

so to answer E every time you would be guaranteed one correct answer in the average 5-question set. but then if you answer E 4 times and leave the 5th problem blank. that gives you an 80% chance of getting one answer correct? or does it just give you an 80% chance of getting E correct and not any answer overall?

so let's say i answer A for number 5. clearly the probability of getting one right in an average 5-question set goes down?

so i have a 20% chance of getting #5 right and an 80% chance of getting 1, 2, 3, or 4 right.

i'm just going to stop though because i do not think i am on the right track if i am even right in the first place. this is frustrating. surely there is a simple permutation or something that will solve this easily?

 

[pwsnafu]

There is a famous test where one student chose C every time. Unfortunately for him the test was true (A) or false (B), so he scored zero. http://funnyexam.com/answers/1618-priceless-b-is-the-new-c".

Also I've had tests where E was "None of the above". In this situation, you can expect E to come up far less than 20%. I've also had a Chem test where B never came up.

of course i have heard that the best way to get the highest score (via guessing) is to just guess the same answer every time, as opposed to guessing randomly on every question

Who told you that? Why should you believe them?

and that makes sense

Why? Sounds like total nonsense to me.

 

[jess1]

ok, if i disregard really specific scenarios like the ones you mentioned. "well I've had a test that wasn't 100% like the hypothetical norm you mentioned so i don't see the point in asking" isn't very helpful.

i mean, if i take every single multiple choice test in history, would it be unreasonable to assume that there would be an even distribution, like each letter would be the correct answer 20% of the time (5 answers to choose from...)? do professors have an inherent bias for against the letter E or something?

so in the average 5 question sample each letter would be the correct answer once. how is that unreasonable? specific scenarios and professors being tricky once in while don't matter and are negligible factors.

at least tell me why that's nonsense instead of just being unhelpful and saying the opposite of what i said. that's just annoying.

even if you disagree with the premise i laid out above (which i think is entirely reasonable), the point of my thread is to use MATH to explain why it is or isn't nonsense, and like i said, i have not taken a stats class, or any math since high school and i really don't have the knowledge to figure this out, so i am asking for someone (you?, if you want to be helpful) to offer a simple equation or something that would either support what I've heard or prove it's nonsense.

i'm not a gullible five year old who believes everything they hear, so please don't need be condescending.

so, it makes sense, given that mean, because: if you guess a or b or c or d or e for five questions, you are guaranteed a correct answer, or in a larger sample size, 20% of correct answers (this is why the SAT subtracts 1/4 of a point for every wrong answer--it is to account for people who just try to guess when they run out of time so if they get 20% of the questions right when there are 5 answers for each question then they don't break even, which would be an AVERAGE), right? so if you guess ANY letter 4 times and a random letter the 5th time, then you don't have that guarantee because the letter that would correspond to your first 4 answers might be the right answer for the one you did not choose that same letter for, and the probability would go down. e, e, e, e, and a. e might be the right answer for number 5;=0 points.

so yes, how do i do this mathematically, basically how likely you are to get 1 question right in the set by choosing the same answer everytime versus guessing randomly. or if you had 100 questions, guessing randomly for all, or choosing B for every single one, since it is likely, unless every professor in the world is a dick, that each letter would be correct 20 times. how this unreasonable? if you think it is, then pretend it isn't, and entertain me with a way to figure out the solution to the problem i have posed, instead of being condescending. thank you.

 

[I_am_learning]

I think if you are randomly guessing answers (yeah its random whether you chose all Ds (d,d,d,d,d,d,d,d...) or just pure 'random' a,b,c,c,,a,e..., beacuse in either case you don't know the correct answer), then chance of getting each answer correct is still 1/5. (asuming 5 options). So I don't think you increase your odds of winning by choosing all the same options. (I myself am learning, so don't take me too seriously)

P.S: Reading your first post, I thought such a humble person you are. Reading your second post revealed your short temperness. If you don't like someone's post, you don't have to shout at that. Just ignore it. Trying to prove urself smart over that poster will only invite conficts. Be calm. (And please don't shout at me for trying to give lectures. :) )

 

[jess1]

thank you

i was having a frustrating day :(

anyways, what you suggested also sounds pretty right to me, idk really.

 

[middlj]

it makes no difference, choosing randomly or the same letter.

 

[chiro]

hello, i made this account just so i could figure this out--i realize people often do that (to make an account without an initial intention of becoming a regular), so i apologize for that; if you feel i am taking advantage of your time and expertise, then i understand. but i am not trying to figure this out for homework or for an upcoming test or anything like that. i just am really interested and don't have the knowledge to figure it out myself and i can't find a good explanation online.

so, of course i have heard that the best way to get the highest score (via guessing) is to just guess the same answer every time, as opposed to guessing randomly on every question, and that makes sense, but what i could not figure out was how to just prove it mathematically. i haven't taken stats :(

i figured the best way to look at it is to take 5 problems with 5 choices each and assume that each letter will be the correct answer 1 time. makes sense right? small sample size that is representative of an infinitely large one?

1) A B C D E
2) A B C D E
3) A B C D E
4) A B C D E
5) A B C D E

so to answer E every time you would be guaranteed one correct answer in the average 5-question set. but then if you answer E 4 times and leave the 5th problem blank. that gives you an 80% chance of getting one answer correct? or does it just give you an 80% chance of getting E correct and not any answer overall?

so let's say i answer A for number 5. clearly the probability of getting one right in an average 5-question set goes down?

so i have a 20% chance of getting #5 right and an 80% chance of getting 1, 2, 3, or 4 right.

i'm just going to stop though because i do not think i am on the right track if i am even right in the first place. this is frustrating. surely there is a simple permutation or something that will solve this easily?

Something purely random like for example a dice will give an output that is not dependent on any prior result. If you assume a balanced die (that is the chance of getting any output is the same), then it won't matter what you pick.

Having said that picking the same number is probably going to better than just picking random numbers every time purely because the probability of getting large strings of the same number goes down exponentially each time, so the chance of getting say 20 2's in a row is very very rare (but it is expected to happen given enough trials).

So I guess in some circumstances the history can help you pick something that if in your favor probabilistically, but in a purely random process, nothing is guaranteed, but probabilistically it makes sense to choose some strategies over others.

 

[I_am_learning]

Here is an expansion:
Assuming that there is 0 probablity that the professor has set options such that all correct answers are option A,then I think its better to go with random than all the same.
The point is, I am trying to make advantage of some knowledge about human behaviour, they can't be totally random, they can't set all answers the same.

 

[middlj]

If the correct answers are distributed at random between the 5 possibilites of A,B,C,D or E; it makes no difference what so ever randomly selecting your answer of choosing a single letter for all.

 

[pwsnafu]

I only read the reply today, so apologies to the lateness.

i mean, if i take every single multiple choice test in history, would it be unreasonable to assume that there would be an even distribution, like each letter would be the correct answer 20% of the time (5 answers to choose from...)? do professors have an inherent bias for against the letter E or something?

Yes, but not necessarily E. Unless we are talking about tests where the professor randomized using a computer, there will be an inherent bias against certain choices. Humans really are that bad at selecting things at random.

As an aside, brute force password attacks exploit this. Certain letter combinations are more likely to be chosen than others, so these get attacked first.

so in the average 5 question sample each letter would be the correct answer once. how is that unreasonable?

at least tell me why that's nonsense instead of just being unhelpful and saying the opposite of what i said. that's just annoying.

This is called http://en.wikipedia.org/wiki/Sampling_bias" . If I choose 5 questions at random there are 3,125 combinations, of which 120 satisfy your criteria. That's only 4%.

even if you disagree with the premise i laid out above (which i think is entirely reasonable), the point of my thread is to use MATH to explain why it is or isn't nonsense, and like i said, i have not taken a stats class, or any math since high school and i really don't have the knowledge to figure this out, so i am asking for someone (you?, if you want to be helpful) to offer a simple equation or something that would either support what I've heard or prove it's nonsense.

Okay, if we assume uniform distribution,

1. If we always select A, the probability that "A is the correct answer" is 20%,
2. If we select at random, the probability of "selecting the correct answer" is 20%.

Its really the same thing: strategy A can be reworded "what is the probability that the professor chooses A?"

i'm not a gullible five year old who believes everything they hear, so please don't need be condescending.

Didn't realize I was.

this is why the SAT subtracts 1/4 of a point for every wrong answer--it is to account for people who just try to guess when they run out of time so if they get 20% of the questions right when there are 5 answers for each question then they don't break even, which would be an AVERAGE),

What's SAT? But yes, the penalty assumes uniform distribution. Standardized tests are computer randomized.

so if you guess ANY letter 4 times and a random letter the 5th time, then you don't have that guarantee because the letter that would correspond to your first 4 answers might be the right answer for the one you did not choose that same letter for, and the probability would go down. e, e, e, e, and a. e might be the right answer for number 5;=0 points.

I don't quite understand what you wrote here, but I have a different criticism. If you are doing probability, the concept of "guarantee" does not exist. Just because there is 100% probability of an event, does not mean that the event is guaranteed to occur.

so yes, how do i do this mathematically, basically how likely you are to get 1 question right in the set by choosing the same answer everytime versus guessing randomly. or if you had 100 questions, guessing randomly for all, or choosing B for every single one, since it is likely, unless every professor in the world is a dick, that each letter would be correct 20 times. how this unreasonable? if you think it is, then pretend it isn't, and entertain me with a way to figure out the solution to the problem i have posed, instead of being condescending. thank you.

To completely not answer the question, you didn't answer my question either. You had a hypothesis that one strategy was quantitatively better than the other. I want to know why it never crossed your mind that maybe the hypothesis was wrong, because, as you claim, you are not a five year old who believes everything you are told. You had a hypothesis, you failed in trying demonstrate the hypothesis, but it seems (from your second post) you had in your mind that you believed the hypothesis was true without doubt.

 

[jess1]

thank you to everyone who has replied. this is exactly what i wanted!

hey man I'm sorry, i was irked that day and took out my frustration and i realize a neutral statement on the internet is easily misread, so my apologies.

i didn't really mean to say either way was more right. i was just going with what i had heard from random people who took high school stats classes. i chose a side to just start from somewhere i guess. (and responded overconfidently and dickishly!)

SAT is just a standardized test that one takes when applying to college.