OT: Blind Guess on a Test!

There was a situation that arose during on of my finals earlier this month where I was clueless as to what the right answer was. I decided that a blind guess was in order but wait the answers confused me. Common knowledge would dictate they are all equal in their percentage to be right but it seems they wern't.

Here is how it was laid out.

A. Answer 1
B. Answer 2
C. All of the Above (Answer 1 and 2)
D. None of the Above (Not Answer 1 and 2)

It seems the dependency of C and D alters the percentages but after working it out I came to the conclusion they were still equal. Can someone explain this mysterious situation to me?

Because there are two choices,answer 1 and answer 2, there are only 4 possible ways to answer; only answer 1, only answer 2, neither 1 or 2, both 1 and 2. Maybe it got confusing because you were reading into it too much.

Suppose the question was: Who has hit 70 or more homeruns in a season?

1. Mark Mcquire
2. Barry Bonds

Answer-

A.Answer 1
B.Answer 2
C.Both 1and 2
D. Neither 1 or 2

A woman who had no idea about the game would have an even percentage no matter what she guessed.

[AaronBrown]

You are correct that there are dependencies, but this only helps you if you have some idea about the answers 1 and 2.

For example, if you think that 1 has a 60% chance of being true and 2 has a 30% chance, then

A. 1 only, 30% to 60%
B. 2 only, 0% to 30%
C. Both, 0% to 30%
D. Neither, 10% to 40%

So A has to be a better guess than B or C. D is only a better guess if you think that if 2 is true then 1 has at least 2/3 chance of being true.

You can also think about the psychology of the test maker. Straightforward professors will ask a question like this most often if the answer is both (this is not as reliable if there are a series of questions like this). Devious ones like to make it neither. Rarely will it be only 1 or only 2, unless there is more than one question of this type.