Seems you have no idea about probability.
Go here for an independent confirmation of the fact that P(event)=1
means it is certain, and that the probability of guessing a correct
answer over four questions is NOT 1.
http://www.ma.hw.ac.uk/~denis/prob/ (its a university site)
> > >Let's try to break this down into real simple pieces so American 12th
> grade
> > >girls may be able understand it.
> > >
> > >If you have a red straw, a green straw, a blue straw, and a white straw,
> and
> > >you ask a student to pick one at random, then if they pick it randomly,
> the
> > >probability of picking the red one is 0.25, and the green one is 0.25,
> and
> > >the blue one is 0.25, and the White one is 0.25.
> > >
> > >If you put all four straws back in your hand and ask them to pick them
> > >randomly again, the probability is the same thing again. If you do it
> two
> > >more times, then the overall probability of picking each color is 1.0: a
> > >red one = 1.0, a green on = 1.0, a blue one = 1.0, and a white one = 1.0.
> >
> >
No no no. Look for simplicities sake lets look at the coin example
again. If a coin is tossed three times then the possible outcomes are
(heads - H, tails -T)
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
8 outcomes (2^3). Right so lets say heads is the correct answer,
according to your reasoning, given that there is a probability of 0.5
of getting a head, then the probability of getting a head after three
tosses is 1.5. Not only is this impossible (nonsensical) from the
sample space above it should be clear that the probability is less
than 1 since there is a 1/8 chance of getting a TTT. i.e. the
probability of getting at least one toss 'correct' is 7/8. Now do you
see how wrong you are in your analysis?
> So let's make it REAL simple. Let's define a simple statement of the
> problem.
>> If you have 100,000 students *randomly guessing* at one multiple choice
> question which has four possible answers (A., B., C., and D.), one of which
> must be selected, then there is only ONE possible outcome:
>> A. gets selected 25,000 times.
>> B. gets selected 25,000 times.
>> C. gets selected 25,000 times.
>> D. gets selected 25,000 times.
>
Your contradicting yourself and you don't even realise it. Given that
the students are guessing 'randomly' then it is by no means certain
that anything of the sort you describe is going to happen (thats what
random means). What probability tells you is what is more or less
likely to happen and what would happen as sample size and repetition
tends toward infinity
> Unless the correct answers are not distributed evenly across A., B., C. and
> D. (i.e., unless the test designers didn't assign the correct answers
> randomly), then there is NO other possible outcome (except for an initial
> minor variation from these figures which would eventually even out over
> time).
>> If the correct answer is B., and this answer is selected by 25,000 girls,
> then you have zero evidence that they properly applied the theories to
> resolving the problem. If they selected this answer 25,750 times, you still
> have no evidence that they understood the principles, or could apply them,
> because such a score would be lower than the 3% standard error. If they
> selected this answer 30,000 times, you are just barely higher than the
> combination of the 25% multiple choice guesses and the 3% standard error,
> which starts to make the score meaningful.
>
Did you pluck standard error out of the air? Standard error is only
introduced when you average results and I see no evidence of that
here, unless you are collating across yeargroups. Is there supposedly
a 3% error in the reporting of test results? I find that hard to
believe as they are likely read by computer and it would mean 3000
students getting erroneous marks.
> BUT--if they selected this answer only 20,000 times, then you have evidence
> that some of them were *misled*, somehow, somewhere, along the way.
>> If you *dispute* this statement of the problem, then post what you believe
> to be the *correct* statement, and quit confusing yourself with probability
> theory which you could never hope to grasp.
>> John Knight
as a test john to see your theories disproven:
from the following four letter strings one is the 'correct' answer.
It doesn't matter what the question or the answers are after all
you're guessing. Once you've answered i'll post the ones I picked out
as 'correct' (prior to you answering of course hebanadl)
P X R A
E F U P
D K O I
L N V O
S P A B
F M S K
Y J H A
E L Z D
