After reading the concern my prompt answer to be $0$ and that to be the answer given.

You are watching: What is the probability of an event that is impossible

But then ns thought various other way, question is probability of difficult event, therefore there are two outcomes possible or difficult (event can be certain or impossible).

Therefore probability of difficult outcome is $\frac12$.

Your an initial answer is right. Your 2nd argument just works come compute the probabilities the equally likely outcomes. for this reason it"s perfectly good to figure out the opportunities of top coming increase from a coin flip. However if one outcome is specified to it is in impossible, climate by definition you are not working with equally most likely outcomes and also so the computation division down.

It relies what you typical by "Probability of difficult event". This is one ambiguous expression which would certainly be interpreted in several different ways:

1) The occasion is recognized ahead that time come be no possible, therefore by definition in stillproud.orgematics, the probability is identified to be 0 which way it can never happen. I suspect most people on this site will walk for this answer. An instance would be illustration a joker from a typical (thus jokerless) $52$ map deck of playing cards. The aint gunna happen.

2) the is not well-known ahead that time if an occasion is feasible or impossible and also you space asking what are the chances it may be impossible. For example, flipping a coin so the lands on its edge. Some people think this is impossible due to the fact that they it seems ~ to always say $50$% possibility heads and $50$% tails but that is dorn cuz it depends where the "lands". I"ve watched a coin land on the side and stay there. What if you upper and lower reversal it and also it floor in soft sand because that example?

3) A details event might seem impossible now however in the future it might be possible. Because that example, that was assumed to be difficult that a dirt bike (motorcycle) could ever carry out a double backflip ramp come ramp in competition but it has actually been done relatively recently (2006 X-games by Travis Pastrana). In reality to me that seems much more like a double reverse flip (facing forwards but flipping backwards). Possible outcomes for this event would it is in success there is no injury, success yet with injury, failure v injury, death....

Is there a time constraint on her event? If not, climate it may simply take a while because that the look at impossible occasion to happen and thus confirm it is possible.

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So mine answer is depending upon what definition/interpretation of "impossible" friend use, the probability have the right to differ although ns wouldn"t know just how to compute any interpretation various other than the interpretation of truly no possible.