# A little question on Probability

1. Feb 20, 2015

### Sundown444

Well, I know that on a scale, a probability of 0 is impossible while a probability of 1 is certain. I do have some things down, but just in case, can anyone here please give me a list of what kinds of events are impossible (0) and what events are certain (1)? I would really appreciate it.

EDIT: And I don't mean card games or dice, but things like sports, cosmic events and natural phenomena like earthquakes and weather.

EDIT: Also, one more thing; What are the odds of a normal human doing some kind of feat that is superhuman in terms of superhuman strength, speed, agility and such? Is that impossible?

Last edited: Feb 21, 2015
2. Feb 21, 2015

### Staff: Mentor

For the real world, probabilities at the extreme edges depend a bit on your philosophical viewpoint. For example, we can all see your post, so are we absolutely certain it exists (as binary representation on a hard drive)? We could all just imagine it, without the post actually being there. Are we even sure we exist? But let's ignore those issues:
No probability for the real world is exactly 0 or 1 unless the event would necessarily violate a fundamental law of physics or is forbidden by logic, then its probability is 0.

In mathematics, it is easier: the probability that an (ideal) six-sided die gives a number from 1 to 6 is exactly 1. The probability that it gives 7 is exactly 0.

That depends on the definition of "superhuman". If you define it as "something humans cannot do at all", then the probability is 0 by definition, "something average humans cannot normally do" gives a small probability.

3. Feb 22, 2015

### h6ss

What makes you think that a probability of 0 is impossible?

4. Feb 22, 2015

### Staff: Mentor

Another relevant concept for very small probabilities is the Boltzmann brain.

Also note that every event "A happens" with a very small probability (or 0) has a corresponding event "A does not happen" with a very large probability (or 1).

5. Feb 22, 2015

### HallsofIvy

Be careful! This is only true if you have a "discrete" probability. If your probability distribution is continuous, this is not true. For example, the probability of choosing any specific number between 0 and 1, with the uniform probability distribution, is 0, yet obviously some number has to be chosen!

How about scoring 1000 points in a football game?

6. Feb 22, 2015

### Staff: Mentor

Not completely impossible. You need a mad goalkeeper and probably a referee to extend the game too long (because 5.4 seconds per goal is a challenge), but it is certainly something that has a non-zero probability.
Related

7. Feb 22, 2015

### Sundown444

Maybe because that is what I read when I looked up probability. Now that you have said that, is there something I am missing?

8. Feb 22, 2015

### h6ss

Only events that are impossible have zero probability, but the converse is not true in general. In fact, it's possible for an event to have probability zero without being the empty event. For example, the event of flipping only tails infinitely many times in a row. This event has probability zero, but it is not empty, because the underlying probability space is the set of all possible ways to flip a coin infinitely many times. What would be impossible, however, is flipping banana, since the coin has only a heads side and a tails side, and no sides marked with the word banana.

9. Feb 23, 2015

### Stephen Tashi

What you "probably" mean is that "an event with probability zero is impossible" - not that "a probability of zero is impossible".

The formal theory of mathematical probability deals with probability spaces and the probability of events in those spaces. It doesn't deal with whether those events actually happen or not. So questions about the possibility or impossibility of events in a probability space involve opinions about applying mathematical probability to situations. They aren't questions that are answered by the axioms of probability theory.