I see your point, but the setter may be baised based on previous answer positions. “Ooh ive not picked D for a while” or “Ive picked too many As so wont pick them again.”
A better way would be to get 60 (or however many questions you need) to independantly write the questions and answer.
Back to Alan and the full exam, one method for questions you dont know fully, is learn how to spot the wrong answers. There are normally 2 obviously wrong answers which then cuts the guesswork to 50/50. By carefully reading the question in respect of the available answers they can become apparent quite quickly and this applies to maths as well.
Reading the question was my big bugbear and often there are negatives (either numberwise, or words like not) in either the question or answers which confuse matters. Getting to grips with that helps with reducing the available choices to guess from.
Martyn,
Oops. If course I should have said 1/16. Duh. Can I plead a moment of total inattention to what I was writing?
If the questions answers are truely randomly assigned then sticking with a single letter is I’m sure the best strategy if the student knows nothing.
In a totally random fashion, with no reference to any of the above (apart from it being mathematical and in some way related to randomness), here’s a paper, “The Gambler’s Ruin with Soft Hearted Adversary”, by R. E. Fagan and T. A. Lehrer written in 1957, and released by the NSA in 2018.
Your attention is drawn to Reference 3 on the final page…
Rick,
I don’t think the Gamblers Choice problem is relevant. The gambler sees the previous results and makes his choice for a future outcome based on previous results. The student doesn’t get the results of each prior question so can’t fall for the gamblers choice syndrome. He doesn’t know for example that A wasn’t the right answer for the last 6 questions so can’t make the choice of picking A in the hope that it will be more likely.
It won’t.
73
Ron
VK3AFW
EDIT. Tom Lehrer, humourous song writer and mathematician, co author of the paper Rick referenced died a few days ago aged 97.
“We’ll all go together when we go”.
Reference 3 is not (as far as anyone has been able to determine) actually referenced anywhere within the paper, but made it into the final copy, and was, apparently, not noticed for sixty years…
…but T. A. Lehrer lived long enough to know that it had finally been spotted.
Yes, that is an example of conditional probability. From there, we quickly come to the most famous theorem of the field, the Bayes’ law, and from there to Bayesian statistics, which one of the most famous ham radio applications, the CW Skimmer, is based on. Amazing!
Rick,
References to unpublished papers like reference 3 ought to raise an eyebrow or two. Where in a library or on line can you find them? A colleague when writing a paper used to add at least one reference to a private communication from some individual which I took as code for I’m sure he would agree with my hypothesis if asked.
Which is why when I had to produce a multiple choice paper it was checked for this.
Sadly fallacious as it’s only obvious if you understand the subject.
And if you have a problem reading and using numbers, an obviously wrong numeric answer where the result is a million times to big or small for example wont appear obviously wrong.
Correctly written multiple choice tests are designed to test your understanding of the subject matter not to answer questions phrased obtusely to catch you out. The tests are not language grammar/understanding tests.
If all 4 answers have the same probability of being right then if I pick A as my answer my chance of being right is 1/4. If I pick B then my chance of being right is 1/4. If I pick C then my chance is 1/4. If I pick D my chance is 1/4. So if I pick an answer at random my chance of being right is 1/4. So it makes no difference whether you stick with the same answer or pick a random one each time.
So the probability of randomly picking A and it being correct is 1/16. But I could also have picked B, C or D and in each case the probability of selecting that answer and it being correct is 1/16. 4 possible answers. 4 * 1/16 = 1/4. The same as sticking with A.
There is a difference between understanding the subject, remembering any equations and having something like Dyscalculia rendering a person unable to perform the calculations.
In a test Full exam done earlier (due to this topic) there was a question along the lines of
A transmitter outputs a power of 5 watts into an antenna with a 3db gain, what is the ERP at the antenna?
A) 3W
B) 5W
C) 10W
d) 15W
Without resorting to any formula or remembering magic numbers in db, it is pretty obvious that 2 answers (A & B) are incorrect since I understand the subject. If I cant do the maths, or remember that 3db is a doubling effect I have increased my chances at a random correct guess.
Yes, but questions are written by people who also make mistakes and some get through. About 30 years ago I took a maths test of 25 multiple choice questions to ascertain then level of maths understanding of a cohort of CIMA students at night school. I scored 24. The one question that was incorrect had that many negatives (in words) in the question that it boiled down to 50/50 if you answered correctly or not (one of the answers being the negative (numerically) of the correct answer with a negative number being possible) .
Even though the test was mostly irrelevant, had no impact on my life in any way shape or form, I still remember it 30 years later. I don’t even remember the question or answers, just the fact that despite understanding the subject I was tripped up by a badly worded question.
In my case, i know that every 3db is a doubling, so i work out how many doublngs it is (in thsi case 1 doubling) and double the number so the answer is 10!
Now, if the question was re-phrased and a fancy calculation was required with a long formulae involved (im sure there is one for this) then thats the point the brain fries, everything becomes mixed up, and it turns into number soup… Like i say, i count change out in shops… physically adding the coins on 1 by 1 to avoid getting it wrong, and the number soup starting!
Im old enough to be branded “stupid and lazy” and told by a multitude of teachers “if I applied/concentrated/listened/payed attention better” I can do the work. these days I would have got help and support and likely got a better understanding, but 80s and 90s aducation was WILD!
You should have tried it in the 60s Alan! Not only would you have been told to concentrate / work harder etc. they have given you regular “jocular” clips round the ears for being lazy and not trying hard enough. Left handed kiddies were still getting hit across the knuckles with a ruler to encourage them to hold a pen correctly in their right hands!
yea, my Dads a southpaw, and that happened to him… clips round the ears were still issued though in the 90s in my school! alot of the teachers were “old school” and didnt like change! They also knew how to cover up wrongdoings by closing ranks… Still, we made the best of it!
Interesting how different people find different things challenging.
Of the sciences, I found both statistics and biology both mysterious and difficult - and dropped them at the earliest possible moment. Endless strings of fact and formulas to remember with no perceivable logic to tie them all together - or none that I could grasp.
Whereas physics, or maths+mechanics (ie. the mathematical basis for Newton to Maxwell via Fourier with stops in between and beyond) I found quite simple - so long as I could remember the logic of how it all worked, I could generally work out the bits I’d forgotten (especially with the help of a good formula cheat sheet!).
All of which served me well in my few years as a telecom engineer.
In my 2½ decades (and counting) in the conservation / wildlife management field however - guess which two disciplines from school I really wish I’d got my head around!
Brilliant, absolutely brilliant Rick. Done while working at the National Security Agency as well. The man had a wicked sense of humour.
I am glad that you injected some humour into this thread before the argument gets too serious.
“Oh, that was easy,” says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.”
― Douglas Adams, The Hitchhiker’s Guide to the Galaxy
My money is on Martyn.
Meanwhile, in the corner of a darkened room, or a damp shed sits a radio waiting to be turned on. In the cupboard a pair of walking boots are gathering dust.
I never liked it at uni and always found it hard. I, for my many sins, did two Maths 0-levels and two Maths A-levels which had different syllabuses. The different syllabuses were broad enough and the were enough questions that we were deliberately only taught part of the syllabus. The exams were of the type answer 5 out of 8 questions. By not doing the stats / probability we ended up with a answer 5 out 6 questions choice. But we were able to skip 1/4 of the syllabus and spent more time on the rest, i.e. we spent 4/4ths of the time on 3/4 of the subject matter.
The problem I had and still have is many probability questions don’t seem intuitive. For which I offer the “Monty Hall Problem” for your consideration.
I was going to go out today, not had the chance for some weeks due many family and home issues. But it was persisting down first thing and now it’s brightened up we have 35mph gusts at sea level and 65mph gusts at sea level predicted for tomorrow. I expect big tree damage with them all covered in leaves etc.
