thanks..but how to figure this out without listing all the possibilities..
should I use AND or OR rule..
I just did it by saying that I have a 50-50 shot on each one and I have 4 questions, so the denominator is clearly 16. The numerator comes from thinking about that there is precisely one way for you to have a correct solution for each question and incorrect for the rest (like 0001 or 0010 in the list).
You can also consider it as an expansion of (F + T)^4 = F^4 + 4*T*F^3 + 6*T^2*F^2 + 4*F*T^3 + T^4 where T is a correct answer and F is an incorrect answer. Then, having T^1 is having one correct and all the rest false. The coefficient of this is 4 so you will have 4 distinct occurrences of having only one question answered correctly.
My probability is a little rusty, but those are two ways that I was thinking of the solution. Would thinking of each "trial" (answering each question) as independent of the other ones help put it in perspective of AND or OR?