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

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But then ns thought various other way, concern is probability of difficult event, for this reason there room two outcomes feasible or impossible (event deserve to be certain or impossible).

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

Your an initial answer is right. Your 2nd argument just works to compute the probabilities of equally most likely outcomes. so it"s perfectly an excellent to figure out the possibilities of heads coming up from a coin flip. But if one result is specified to it is in impossible, then by an interpretation you space not working through equally most likely outcomes and also so the computation division down.

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

1) The occasion is recognized ahead the time come be no possible, because of this by definition in snucongo.orgematics, the probability is characterized to be 0 which method it deserve to never happen. I doubt most people on this website will walk for this answer. An example would be drawing a joker native a typical (thus jokerless) \$52\$ card deck of play cards. The aint gunna happen.

2) that is not well-known ahead the time if an event is possible or impossible and you are asking what space the opportunities it may be impossible. For example, flipping a coin so the lands on its edge. Some civilization think this is impossible because they it seems to be ~ to constantly say \$50\$% chance heads and \$50\$% tails yet that is not correct cuz it counts where that "lands". I"ve viewed a coin floor on its side and also stay there. What if you upper and lower reversal it and also it lands in soft sand because that example?

3) A specific event may seem difficult now however in the future it may be possible. For example, that was believed to be impossible that a dirt bike (motorcycle) could ever do a twin backflip ramp to ramp in competition yet it has been done relatively recently (2006 X-games by Travis Pastrana). In reality to me that seems an ext like a double reverse upper and lower reversal (facing forwards however flipping backwards). Possible outcomes because that this occasion would it is in success there is no injury, success however with injury, failure with injury, death....

Is there a time constraint on your event? If not, climate it may just take a while because that the seemingly impossible occasion to happen and thus check it is possible.

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So my answer is relying on what definition/interpretation that "impossible" friend use, the probability deserve to differ although i wouldn"t know exactly how to compute any interpretation other than the translate of truly not possible.