After reading the question my immediate answer was \$0\$ and also that to be the answer given.

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But then ns thought other way, inquiry is probability of impossible event, for this reason there are two outcomes possible or difficult (event can be particular or impossible).

Therefore probability of difficult outcome is \$frac12\$.

Can that also be answer?

Your first answer is right. Your 2nd argument just works come compute the probabilities the equally likely outcomes. so it"s perfectly good to figure out the possibilities of heads coming up from a coin flip. However if one outcome is mentioned to it is in impossible, climate by an interpretation you space not working v equally likely outcomes and also so the computation division down.

It relies what you mean by "Probability of impossible event". This is one ambiguous phrase which would be taken in several various ways:

1) The occasion is well-known ahead of time come be not possible, thus by meaning in historicsweetsballroom.comematics, the probability is characterized to be 0 which means it deserve to never happen. I suspect most world on this site will go for this answer. An instance would be illustration a joker from a typical (thus jokerless) \$52\$ map deck of play cards. That aint gunna happen.

2) that is not recognized ahead the time if an event is possible or impossible and you space asking what space the opportunities it may be impossible. For example, flipping a coin so that lands on its edge. Some civilization think this is impossible since they it seems to be ~ to always say \$50\$% possibility heads and \$50\$% tails yet that is wrong cuz it depends where that "lands". I"ve watched a coin land on the side and stay there. What if you upper and lower reversal it and also it lands in soft sand for example?

3) A particular event may seem impossible now but in the future it may be possible. Because that example, that was assumed to be difficult that a dust bike (motorcycle) might ever carry out a twin backflip ramp come ramp in competition yet it has actually been done reasonably recently (2006 X-games by Travis Pastrana). Actually to me the seems an ext like a double reverse flip (facing forwards yet flipping backwards). Possible outcomes because that this occasion would be success there is no injury, success but with injury, failure with injury, death....

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

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So mine answer is relying on what definition/interpretation the "impossible" girlfriend use, the probability deserve to differ although ns wouldn"t know just how to compute any kind of interpretation various other than the interpretation of truly no possible.