No wonder I failed…. according to statistics.
note : this is for entertainment purposes only. Nothing to be taken seriously.
I got 4 out of 10 for my STAT101 (Statistics) quiz. So sad. Curious about how I did so badly (like other students in my class), I tried to analyze it.Multiple choice questions are examples of Bernoulli Trial. There are only 2 possible outcomes : right or wrong. According to what I learned in stats, to calculate how big is the probability to get a certain number of successes in a certain number of experiments, we need to use Binomial Distribution.
Confused? Don’t be. 
Regarding my MCQ-style test, I had 10 questions on the test. Now, to calculate the probability of having all of the questions answered right, we should use Binomial Distribution.
Binomial Distribution is represented by :
where
(or maybe better known as nCk)
while
n = the number of experiments.
k = the number of successes, can be modified according to our need. (For example if we want to calculate the probability of getting 2 answers right, the k will be 2, and so on)
p = the probability of success in each experiment.
In the case of my MCQ stats quiz which had 10 questions with four choices each, thus :
n = the number of questions, which is 10.
k = 10 (since we want to calculate the probability of getting all the answers right)
p = since there are 4 choices, the probability is 1 out of 4 (1/4)
Okay, now let’s start the calculation..
Let X denote the number of getting the answer of the question right.
Then
Since 10C10 results as 1 and so does 3/4 to the power of 0, what’s left is 1/4 to the power of 10.
And the result is…………………
(use the google calculator, or your own calculator, if you’re too curious)
………………………………. (the tension continues)
9.53674316 × 10-7 which equals to 9.53674316 × 10-5 percent.
Ha.
So the probability of having all answers right from 4 choices, ten questions MCQ test is just 9.53674316 × 10-5 percent.
No wonder I failed.
Technorati Tags: math, statistics, equation, test, MCQ
additional note : the p is only 1/4 when we really really randomly choose. My bad. But FYI, for that stats quiz I really did randomly choose several numbers.
No related posts.
Related posts brought to you by Yet Another Related Posts Plugin.
9 Responses to “No wonder I failed…. according to statistics.”
Leave a Reply
on 
on 
Aditya
on February 15th, 2007
I think you need to study more for your stats.
That kind of seemingly-complex-but-actually-simple calculation cannot fool me. In fact, you get your assumptions dead wrong since the second paragraph.
Study more.
^sylv^
given the fact I got 4 out of 10, yeah I do think I need study more. Eh but I’m not fooling you. The example given to me about the Binomial Distribution also talks about MCQ style tests. Really loh.
ivan
on February 15th, 2007
hahahahaha …… dasar =) …. ada2 aja
meli
on February 15th, 2007
give up dah =))
Aditya
on February 15th, 2007
^sylv^
given the fact I got 4 out of 10, yeah I do think I need study more. Eh but I’m not fooling you. The example given to me about the Binomial Distribution also talks about MCQ style tests. Really loh.
[AL]
err… no.
in the equation…
you imply that your failure is statistically unavoidable.
Which is super duper WRONG (since p will be way above 0.25 if you study properly)
So… kindly press alt-f4 or ctrl-alt-del followed by a series of enter button…
(since you have conveniently disable Acer’s built in auto-off feature)
and study
^sylv^
the p is 1/4 because there can only be one correct answer out of 4 choices. No matter how hard I study, or how short is my sleeping time, there would not be 2 or 3 correct answers in one question.
harph
on February 15th, 2007
Dah lama ga mampir ke sini.. pa kabar nya dikau?
Duh.. jangan bahas math deh…. i m sick of it… =_=
Aditya
on February 15th, 2007
^sylv^
the p is 1/4 because there can only be one correct answer out of 4 choices. No matter how hard I study, or how short is my sleeping time, there would not be 2 or 3 correct answers in one question.
[AL]
WRONG concept…
p=0.25 if you only make wild guess (never study)
p0.25 if you study and decided to do better
for example, what is the probability of you answering this questions below correctly (without cheating) – there is only one correct answer…
Question A
1 + 1 =
a. 1
b. 2
c. 3
d. 4
Question B
What’s the value of Chandrasekar Limit?
a. (2/μe)2 · 2.85 · 10^29
b. (2/μe)2 · 2.85 · 10^30
c. (2/μe)2 · 2.85 · 10^31
d. none of the above
Assuming you have finished your primary education.
p for answering Question A should be very close to 1.0
(since you have studied it before)
ANS: B
Assuming all SMU students are science retard
p for answering Question B should be 0.25 (wild guess)
ANS: B
NRN
nay min thu
on February 16th, 2007
i hated stats in my first year.. but i managed to pull thru..
=)
chillycraps
on February 16th, 2007
haha Sylv, p=0.25 assuming you really didn’t study at all, ie just anyhow pick one choice.
but this entry sure cracks me up with all the equations!
imambenjol
on February 17th, 2007
keren 4 dari 10! pertahankan prestasimu nak! lol
^sylv^
masih mending loh. yang lain dapet 2. =P