Average test score for random guesses on multiple choice.

Question

Suppose there is a test with ten multiple choice questions. Each question has four options (and only one correct answer).

What is the average score of the test?

I know that there are 4^10 (= ~ 1M) possible answer combinations, but things get a bit fuzzy after that.

Answer 1

You're very close. Using the word combination here might not be the best idea. Why not (think about order)? How many answer _______ can be correct?

To verify your answer, you can try solving it a different way. What is the probability of correctly guessing the answer for a single question? Is guessing correctly on Problem 1 dependent on guessing correctly on any other problem? Is it the same for all 10 problems?