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.
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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.