Can the probability of an outcome be zero?

Answer 1

Yes. But there are at times philosophical problems at stating that the probability of an outcome that either has never been observed is zero. As a supposition or assumption, we can say that a particular outcome is zero, but how do we prove it? For example, I might believe that it is physically impossible for a person to weigh more than 1,000 lbs as no human on earth weighs that much, but if just one person weighs more than a 1,000 lbs, I have to accept that this outcome has a finite probability. We can come to the conclusion of impossibility by our cumulative knowledge. For example, it is impossible for a person to run 200 mph. World athelete's running speeds are very close, far below 200 mph. I can't prove it rigorously, but it is a rational conclusion based on our knowledge. To most people, if something has a chance of success of one in a billion or one in a trillion, this is close enough to impossible. However, even with these low probabilities, the result is still not impossible. For example, most people would think that winning the lotto 10 times in a row would be impossible, but the probability is above zero, therefor possible.