Probability of impossible event. There is question in my book: Probability of impossible event is?
After reading the question my instant answer was $0$ and that was the answer given.
But then i thought other way, question is probability of impossible event, so there are two outcomes possible or impossible (event can be certain or impossible).
Therefore probability of impossible outcome is $\frac{1}{2}$.
Can that also be answer?  

Your first answer is right. Your second argument only works to compute the probabilities of equally likely outcomes. So it's perfectly good to figure out the chances of heads coming up from a coin flip. But if one outcome is specified to be impossible, then by definition you are not working with equally likely outcomes and so the computation breaks down.
