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05 Oct 2004, 22:21
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True story--and good GMAT problem-
friend in high school years ago took a 100 question multiple choice test.
Each question has answer options A,B,C,D, and E. So 5 choices.
He scored a 61% on the test by filling in "ACDC" for answers
1, 2,3, and 4, respectively, and he repeated this till the end of the test.
so 25 sets of ACDC. incredible! (yes, ACDC after the Australian band.)
What is the probability of this?
pretty simple, right?
friend in high school years ago took a 100 question multiple choice test.
Each question has answer options A,B,C,D, and E. So 5 choices.
He scored a 61% on the test by filling in "ACDC" for answers
1, 2,3, and 4, respectively, and he repeated this till the end of the test.
so 25 sets of ACDC. incredible! (yes, ACDC after the Australian band.)
What is the probability of this?
pretty simple, right?
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06 Oct 2004, 12:32
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What the heck...I'll take a crack at it.
First off, I'm assuming that the answer choice is randomly generating (i.e. there is always a 1/5 chance that any random answer picked is correct).
Now that the assumptions are out of the way:
The chance of getting the 1st 61 questions right and the last 39 questions wrong is (1/5)^61 * (4/5)^39 = 3.831 * 10^-47.
Next: figure out the number of combinations that you can get 61 questions right and 39 questions wrong.
100!/61!39! = 9.014*10^27
We want to find p(combo1) OR p(combo2) OR p(combo3)...OR P(combo 9*10^27)
Since all combos have the same liklihood of occuring, the probability of scoring 61% on a 100 question test using random guesses (guessing ACDC without looking at the question should have the same probability of guessing all As or Bs) would be 3.831*10^-47 * 9.014 *10^27 = 3.453 *10^-19.
In other words there would be a 0.00000000000000003453% of getting 61 right on a 100 question test where the right answer choices are randomly and all answers are bubbled in randomly.
Anyone care to share their ideas?
First off, I'm assuming that the answer choice is randomly generating (i.e. there is always a 1/5 chance that any random answer picked is correct).
Now that the assumptions are out of the way:
The chance of getting the 1st 61 questions right and the last 39 questions wrong is (1/5)^61 * (4/5)^39 = 3.831 * 10^-47.
Next: figure out the number of combinations that you can get 61 questions right and 39 questions wrong.
100!/61!39! = 9.014*10^27
We want to find p(combo1) OR p(combo2) OR p(combo3)...OR P(combo 9*10^27)
Since all combos have the same liklihood of occuring, the probability of scoring 61% on a 100 question test using random guesses (guessing ACDC without looking at the question should have the same probability of guessing all As or Bs) would be 3.831*10^-47 * 9.014 *10^27 = 3.453 *10^-19.
In other words there would be a 0.00000000000000003453% of getting 61 right on a 100 question test where the right answer choices are randomly and all answers are bubbled in randomly.
Anyone care to share their ideas?
