"John Knight" <johnknight at usa.com> wrote:
>The statement is that the probability is 1.0 that you'll get one answer
>correct if you just guess on four different questions with four multiple
>choice answers. That's much different than you are "CERTAIN to get one
>answer correct".
No it isn't, because a probability of 1.0 is the definition of "certainty".
>Obviously you were never taught probabilities and statistics.
And obviously you have forgotten the lowest lessons.
>This is the
>most basic principle possible. No, it doesn't happen that way EVERY time,
>but over a long series of questions and answers, it will eventually end up
>this way.
If the probability is 1.0 that they will get 1 answer correct if they guess 4
times, then EVERY time someone answers 4 questions by guessing, they will get
one answer correct, never 0 and never more than 1 correct.
That is the definition of probability, 1.0
>> You still have yet to address the conclusion that if 100% answer
>> correctly no-one guessed and if 0% answer correctly then something
>> very strange happens as the population taking the test suddenly
>> increases by a third but their papers are somehow lost. As you might
>> see from working with the latter case, your analysis does not hold.
>>It's not clear what you're saying, but the last part of your statement means
>that it's obviously wrong--and it's ceretainly not consistent with the
>original statement. Consider the two extremes:
>>If zero percent get a four part multiple choice question wrong, then they're
>scoring 25% lower than if they'd just guessed, in which event might conclude
>that there's a high probability that they were taught the wrong thing if
>everyone selected just one wrong answer. The other extreme is if 50% get
>the answer correct, and the rest of the answers are spread evenly over the
>other three answers, then this *is* an indication that 50% understood the
>problem [50% guessed wrong, x = total percent who guessed, .25x = the total
>number who guessed correctly, .75x = the percent who guessed incorrectly, x
>= 66.67 percent = total guesses, .25x = 16.7 percent = percent who guessed
>correctly, and .75x = 50 percent].
>>So at 50% correct, guesses don't influence the score, and you don't have to
>worry that "something very strange happens as the population taking the test
>suddenly increases by a third but their papers are somehow lost".
If, in your example, 66.67 percent guessed, with 16.7% thereby guessing
correctly, then of the 33.3% that did not guess, 100% were correct. Thus
"guessing" lowered the score from 100% to 50% which means that guesses DID
influence the score.
But of course you exclude the possibilities that some who got it correct were
taught incorrectly but got the right answer through erroneous logic, that
some who got it incorrect were taught correctly but applied erroneous logic.
And it excludes people like you that, regardless of what they were taught,
pursue really weird logic and end up with nonsense.
lojbab
