system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why is it recommended to guess the same letter when running out of time during a multiple choice test?

I guess I can sort of see why this method works, but I can't explain it, which makes me wonder if there are actual statistics and mathematics to prove how. Besides this method being faster than randomly guessing for each answer, supposedly this method *should* result in a higher percentage of correct answers. My intuition agrees, but when I think about it, wouldn't every guess on a question have an equal 25% chance of being correct? Can someone please prove or disprove this and explain why?
gpt
On a twenty question test, suppose you've answered 16 of the questions the best you can, but have no clue on the last four--you can't eliminate a *single* answer. 

For each individual question, an answer has a 25% chance of being right, so if you pick B, 1/4 times you'll be correct. The formula for looking at multiple questions will be

  >  p(r) = nCr * p^r * q^(n-r)
    

where
>r=# of questions

>nCr=# needed correct (which can be 1, 2, 3, or 4), or n! / r!(n-r)!

>p is probability of getting an answer correct, .25

>q is probability of getting an answer incorrect, .75

So the probability of getting **all four** correct is 0.00390625 - or, low. The probability of getting **one or more** right is 0.68359375, or, pretty good. The likelihood of getting all four answers wrong is (3/4)^4 = 0.31640625 (alternatively, 1-0.68359375)

Looking at the specifics of your question, it comes from most tests not being truly random. A handwritten test with human selected answers will not be random, which is where things like 'guess C always' come from. 

A computer generated test will be random, and because each question is independent from another, it doesn't really matter what answer you pick.