Combinatorics Related Question

[dagr8est]

Say you had 10 questions with 5 possible letter answers for each question. Mathematically, there would be 5^10 ways to fill out an answer key and each of those answer keys would have the same probability of scoring 10/10.

I tried randomly guessing answers using different answer keys and found that I constantly got 2-3 correct when I chose 10 of the same letter. However when I chose letters randomly, I usually got 0-1 correct.

Is choosing 10 of the same letter a better strategy or am I just bad at randomly guessing?

 

[Unco]

Provided the letter corresponding to the correct answer for each question is randomly chosen, there can be no strategy to improve your chances by guessing (except studying beforehand and improving your guessing, of course).

Try conducting an experiment using the random number generator on your calculator to choose randomly, versus choosing one column (eg. all A's) with the different answer keys; you'll need quite a few.

 

[Gene]

Also you could see what you get if you had choosen a different letter. 2 is what you should average no matter what method you use.
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Gene