Why is not the answer to all probability questions 1/2. Ok, I know this is wrong, but I want someone to tell me why. 
Let's take a normal heads tails example of a fair coin. The probability of getting head = 1/2. And I write this is because, either it will be heads, or not. Hence two cases that makes it 1/2.
Now, I know I can't do this to all the cases. For example, the probability of getting a 2 when I roll a dice. I know the answer is 1/6 but why can't I do, either the outcome will be 2 or not. And in that case, my probability is 1/2.

Probability is the study of "making the most out of insufficient information".  If you knew all relevant information about a situation, then the probability of an outcome is always 100% or 0%.  
The reason your answer isn't 1/2 for rolling the dice is because you aren't using all information available.  In fact, if you gain more information (weights of the dice, staring position, initial direction of the throw) then the probability goes from 1/6 towards 100% or towards 0%.
There is no such thing as "the probability of an event".  It is "the probability of an even given what we know".  Two different people can get 2 different probabilities just because they have differing degrees of knowledge.
