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 Probability of Guessing   « on: May 23rd, 2014, 3:16pm » Quote Modify

This is a *classic* but I couldn't find it in the forums.  Maybe I am too new at using the search feature

Anyways:

If you were to choose an answer to this question at random what is the probability that it would be correct?

a) 25%
b) 50%
c) 100%
d) 25%
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Grimbal
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 Re: Probability of Guessing   « Reply #1 on: May 23rd, 2014, 3:55pm » Quote Modify

None of the answers is "correct".
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towr
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 Re: Probability of Guessing   « Reply #2 on: May 24th, 2014, 12:43am » Quote Modify

We'd have to know what makes an answer correct (as well as the random distribution)

Bureaucratically speaking, the right answer is whichever is on the answer sheet, even if it's wrong. If the answer sheet says a, then even though c is also 25% it wouldn't be marked correct.
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EdwardSmith
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 Re: Probability of Guessing   « Reply #3 on: Jul 6th, 2014, 8:49am » Quote Modify

The answer would sometimes be A or D.
Occasionally B.
Or C only on the first few guesses.
But after several guesses the chance of your guess being correct would diminish.
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Lupin
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 Re: Probability of Guessing   « Reply #4 on: Jul 10th, 2014, 8:01pm » Quote Modify

This is a logical paradox: if you don’t know what the question, and/or the answer, for that matter,  is, how can you determine the probability of it being correct?  However, if the probability that it would be correct is one (and only one) of the four choices then you have 25% (1 of 4) of choosing the correct choice. Then, if only one choice is correct, A and D are the same and cannot be the correct choice.   You are left with B (40%) or C (100%)   I don’t think a probability of 100% is possible in any given situation, so I think the choice should be B (50%) in 1:2.  I don’t think this is the correct answer, but it’s something  I considered.  Then, again, if it is a paradox, the probability should be 0%.

A person asked Einstein, “What is the best question to ask and what is the correct answer to it?”  And Einstein replied, "The best question to ask is the one you just did and the correct answer to it is the one I gave.”
 « Last Edit: Jul 10th, 2014, 9:30pm by Lupin » IP Logged
rmsgrey
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 Re: Probability of Guessing   « Reply #5 on: Jul 11th, 2014, 2:01am » Quote Modify

Is it ever correct to choose an answer at random?
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dudiobugtron
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 Re: Probability of Guessing   « Reply #6 on: Jul 11th, 2014, 2:12am » Quote Modify

on Jul 11th, 2014, 2:01am, rmsgrey wrote:
 Is it ever correct to choose an answer at random?

*flips a coin* ... Yes.
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Uberpuzzler

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 Re: Probability of Guessing   « Reply #7 on: Jul 11th, 2014, 7:14am » Quote Modify

Is it ever correct to choose an answer?
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dudiobugtron
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 Re: Probability of Guessing   « Reply #8 on: Jul 11th, 2014, 1:46pm » Quote Modify

on Jul 11th, 2014, 7:14am, rloginunix wrote:
 Is it ever correct to choose an answer?

If the question prompts you to make a choice, then yes.  eg: What would you like for dinner?
 « Last Edit: Jul 11th, 2014, 1:47pm by dudiobugtron » IP Logged
towr
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 Re: Probability of Guessing   « Reply #9 on: Jul 12th, 2014, 1:42am » Quote Modify

Yeah, so given a multiple-choice question, choosing does seem like an appropriate response.
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Uberpuzzler

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 Re: Probability of Guessing   « Reply #10 on: Jul 12th, 2014, 9:20am » Quote Modify

on Jul 11th, 2014, 1:46pm, dudiobugtron wrote:
 What would you like for dinner?

Meat!

See how I deduced my answer? Hungry and meatless childhood in the Soviet Union - ability to buy the real thing here in US ...

I equated choosing to guessing (strengthening rmsgrey's question) implying that reasoning, however well concealed, is or must be always there. Even on the multiple choice questions.

May be it deserves its own thread elsewhere, "Academic Test Types In Different Countries" or some such, but you, guys, take the multiple choice tests for granted while I didn't even know that they existed in this Universe until I came to US. It was a seismic cultural shift. In my grade school the only way the tests were administered was thus.

The only thing that you get is the problem statement. That's it. No answers or hints of any kind. Pen, paper. You were supposed to deduce the answer on your own, step by step, blow by blow, put it all down on paper and submit all of this to your teacher for inspection and grading (5=A, 4=B, 3=C, 2=F, 1=bring your parents). Teachers were mostly interested in hows and whys, not whats. (I was bad news in the grade school, by the way).

My college entrance exams were in the same format. Math, physics, composition. Several college seal stamped sheets of paper, 5 hours, 4 problems. Problem statement, no answers, no hints. The admission committee wanted to see all of your step by step in its entirety. Same drill during the college years.

At first I even despised the multiple choice questions thinking "Ha! This is stupid. There's no thinking involved here. One must deduce the answer from scratch. Here they practically give you the answer, even if it's 'none of the above'". Now, over the years, I of course changed my stance but you see where I was coming from.

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towr
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 Re: Probability of Guessing   « Reply #11 on: Jul 12th, 2014, 1:09pm » Quote Modify

I'd say deduction is a way of choosing an answer. (You can even see it as traveling along a path in a decision tree with many leaf-nodes ending in right and wrong answers, and each deduction step -- if taken correctly -- taking you closer to the right choice)

But I have read some article or book once where someone made a similar distinction between picking and choosing; the first being guessed the other reasoned.
On the other hand, an educated guess is reasoned as well. It's mostly a matter of degrees of certainty in the facts you start with and the steps you apply.
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dudiobugtron
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 Re: Probability of Guessing   « Reply #12 on: Jul 12th, 2014, 1:46pm » Quote Modify

Quote:

I enjoyed it a lot, thanks!

In the New Zealand Education system (although it's never been as authoritarian here as the Soviet Union was, of course), we mostly have problem questions with no hints, and children (and adults still studying) are expected to work out the answer for themselves.  The focus is on the process.  I think the predilection for Multiple-choice questions is mostly a US thing.

I too have always been rather wary of multiple-choice questions.  Although I agree that, if written well, 'choose the best answer' multiple-choice questions can often be even harder than the equivalent 'short answer' question, since you can be misled by answers which 'seem right'.
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 Re: Probability of Guessing   « Reply #13 on: Jul 12th, 2014, 3:12pm » Quote Modify

Hm, interesting. That's one puzzle I can't solve. Soviet Union with its love for all things authoritarian, absence of pluralism and choice, did not have one centralized college entrance exam system - each college rolled its own (I'm talking mid 1980-ies).

In US, however, where two schools in the same town have two different curricula, there is a centralized college entrance exam system - SAT. In the early days it stood for Scholastic Aptitude Test, nowadays it's mostly an empty acronym.

Its Math section has 54 questions given over two 25-minute and one 20-minute periods. 70 minutes total. So on average that's 77.78 seconds per question. Each question is relatively "easy" but there are many of them and you don't have much time.

If you don't mind me asking, how does the New Zealand college entrance system work?
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rmsgrey
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 Re: Probability of Guessing   « Reply #14 on: Jul 12th, 2014, 6:23pm » Quote Modify

Here in the UK, most exam questions break things down step by step for you, so, you'll be asked for something like the statement of Newton's Third Law, then given a question about the forces acting on a body, then another one that requires you to apply N3 to the previous answer, then...

It's pretty rare to be expected to provide more than 3-4 marks worth of answer at once, with the individual parts adding up to a question worth 10-20 marks. You'll also often see "Use your answer to b(iii) to calculate X. If you didn't get an answer, use 42.0 instead." so people who get stuck at an earlier stage can do the later parts anyway (in this example, the correct answer to b(iii) was probably 36.8 or similar - they explicitly give you an incorrect value so you can't just copy it for credit in the earlier part)

Once you get to university, it's more likely that you'll get an exam question that just expects you to do 10-20 marks worth in one go, without any waypoints or interjections from the exam-setter.

In my school career, multiple choice papers were rare - the main example which comes to mind was the UKSMC (UK Schools Maths Challenge) and related - a 25 question 5-answer multiple choice paper of tricky maths questions intended to be solvable for bright students of the target age, so educated guesses and deduction are entirely acceptable and even expected.
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dudiobugtron
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 Re: Probability of Guessing   « Reply #15 on: Jul 13th, 2014, 2:46am » Quote Modify

on Jul 12th, 2014, 3:12pm, rloginunix wrote:
 If you don't mind me asking, how does the New Zealand college entrance system work?

Is 'college' University?  In New Zealand we call Secondary Schools 'colleges', so it's a bit confusing!

To answer your question - in secondary schools, each subject has a number of different 'achievement standards', which are basically modules on a specific topic.  eg, in maths you might have a trigonometry standard, and a linear algebra one, etc...

Each standard is worth a certain number of credits if you pass it.

Getting University Entrance in New Zealand requires getting a number of different credits across your subjects at secondary school; including a quota of 'literacy' and 'numeracy' credits.
Some courses require a particular set of achievement standards, or credits in particular subjects, in addition to University entrance.  For example, you would probably need to have passed some particular calculus or physics achievement standards in order to get into Engineering.
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Uberpuzzler

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 Re: Probability of Guessing   « Reply #16 on: Jul 14th, 2014, 10:50am » Quote Modify

Thank you rmsgrey and thank you dudiobugtron. I'm always interested in learning how these things work in other countries. Seemingly simple subject but such a variety of implementations!

In my mind "college" and "University" are the same thing. In my time there was no word "college". "Institute" mostly, sometimes "University". Basically, you went to a grade school from the age of 7 for 10 years, Monday through Saturday (6 days a week). Then at 17 you (if desired) would enter "institute" (or "University"). Five and a half years, till you're about 22-23. There were no gradations like in the US: Associate degree (2years), Bachelor's (another 2), Master's (another 2), etc.

Coming back to this question. I think the best way to deal with the multiple choice questions is to 1) read the problem statement, 2) do not read the answers list, 3) solve the problem on your own, 4) compare results.
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dudiobugtron
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 Re: Probability of Guessing   « Reply #17 on: Jul 14th, 2014, 2:01pm » Quote Modify

on Jul 14th, 2014, 10:50am, rloginunix wrote:
 Coming back to this question. I think the best way to deal with the multiple choice questions is to 1) read the problem statement, 2) do not read the answers list, 3) solve the problem on your own, 4) compare results.

This is a good approach for many types of multiple-choice questions.

However, for questions where answers are easy to verify, but hard to generate (P v NP anyone?), looking at the list of possible answers can save you a lot of time.

Silly but illustrative example:
What is 61245 squared?
a) 3750950023
b) 3750950024
c) 3750950025
d) 3750950026
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Uberpuzzler

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 Re: Probability of Guessing   « Reply #18 on: Jul 15th, 2014, 4:45pm » Quote Modify

We instantly eliminate a), b), d) and zoom in on c). Since there's no "e) none of the above" c) must be the answer.

Though in the back of my mind I (instinctively) would want to double check anyway, , but I see your point.
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