My Grey World

15 Feb, 2007

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^-7which equals to 9.53674316 × 10^-5percent.

Ha.

So the probability of having all answers right from 4 choices, ten questions MCQ test is just 9.53674316 × 10^-5percent.

^{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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