A Bit of Maths...

There are 30 objective questions in an Economics examination paper.

Let X be the number of questions that I scored correct in the paper.
Therefore X~N(30, 0.25)

0.25 is the probability that I will get a question correct.
0.75 is the probability that I will get a question wrong.

If I magically manage to get every single question correct, the probability for that event occuring will be...
P(X=30) = ³⁰C₃₀ (0.25)³⁰ (0.75)⁰ = 0.00000000000000000086736

Let's say that I know only half of the paper. So, I estimate that I'll get 15 questions correct...
P(X=15) = ³⁰C₁₅ (0.25)¹⁵ (0.75)¹⁵ = 0.000000000012445

Then let's say that the gods frown on me, and I shockingly end up with not even a single question correct...
P(X=0) = ³⁰C₀ (0.25)⁰ (0.75)³⁰ = 0.00017858

Hence, the probability of me having no questions correct is definitely higher than me mysteriously scoring all questions correct by random choosing.

I'm so doomed in my Economics.