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.

We cannot calculate a probability without using other probabilities in the calculation.
When we say that a coin has $P(H)=1/2$, or a die has $P(2)=1/6$ that is not something we learn using probability theory, it is an assumption about physics.
We assume that the die can only land with a face up, and we assume that all faces are equal in geometry and weight distribution, and therefore that the sum of probability for the faces is 1, and that the probability is the same for all 6 faces. Pure physics.
If I roll two dice I believe that each of them exert the same probabilities as a single die, and that they do this independently of one another. This is not something I can learn using probability theory either, it is an assumption about physics that the dice do not coordinate their rolls.
Once we have all these assumptions about die physics we can do all the cool die equity calculations using probability theory.
Unlike the rest of the world, dice are made for producing independent stochastic variables, the assumptions about die rolls have a solid foundation in physics that is pretty much undisputed. But when we try to figure the probabilities of something with real world relevance simple physics will not suffice, rather we might have to rely on psychology, sociology, economics or palaeontology. Putting probabilities on different outcomes is often guesswork, and different variables have all sorts of odd correlations, meaning that basic probability theory (which always assume independent variables) won't work.
When the coin argument seems to be universally applicable it is actually because it is a false argument, it just happens to produce the right result for fair coins.
