Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2

If you're curious, I never ended up making the third part of this. Or rather, I made part of it and thought it wasn't very good. The plan is to put together something like a probability series this year, where the beta distribution will surely be one of the topics. Thank you for your patience!

almost-impossible is only almost impossible

Actually I call these infitsmall chances
ε% Chance
1/Infinity% chance
1/ω% Chance

Any truly random draw from a continuous probability function is a transcendental number.

Very impressive animation and interpretation of the statistical concepts!

Dude you got me out of a break up when I was 20, and again at 26

These videos are the best product of 4 centuries worth of science

Oh that was a low-down dirty trick. The first video really made me want to understand why adding 1 positive and 1 negative review to a set of reviews for an Amazon product somehow gives a better estimate of what your own experience is likely to be. And we still don’t have an answer! Pure evil. If anyone can point me at the explanation I’d be grateful.

If I had 4 balls 3 of them would be blue right now after this blue balling.

Someone here read PDF as a file type

Where is the part 3 ?

So you're telling me there's a chance

It's weird actually knowing something on your channel before watching the video

Paradoxes dont exist they are just flaws in our logic

This was my a level stats

Probability is a man made concept that has nothing to do with reality. It is based on the false premise of repeated trials.

i think the probability that I can watch this till the end without falling asleep is 0

There is no physical application in the real world that is actually continuous. Everything is quantized into sections, so nothing possible actually has a probability of 0 unless you model it approximately as a continuous system.

Seems like ten minutes of semantic hocus-pocus to try to justify the absurd claim made in the title.

Nice man ,,,👍

her: there is zero chance I'm dating you.
me: shows this video

Asking how the prob of P(X=3) is is like asking how many m in length you need for 10 m² in area. It's not the same meassuring unit at this point. Thats why you need infinity of them to let them add up to a finite value. It simply doesn't fit togehter. P(2.5<=x<3.5) would be asking for right dimention.

Thank you.

This is a well made video, but the title feels awful.

For anyone else who was interested in the true probability of a zero chance, I think a fun thinking exercise is the chance that two atoms suddenly switch places, and the chance that in a game, an enemy drops something that doesnt exist in the game‘s code, and which is rarer

well the properbility of an Earthlike planet to exist anywhere in the universe is zero, but we know that one such planet exist

Is it truly correct to say that the probability of a specific value is 0% though or would it be better to say that it is infinitesimaly small? It may sound the same but intuitively it makes sense that if you pick some value, even though it is only one in infinite possibilities, you are getting more chances than not picking anything

The probability of me missing the board is 1

Oh thats why I was losing some 100% chance to win battles in civilization 4

So you're basically telling that because you're to lazy to make the exact answer to your own question "what is the probability of those probabilities" because you definitely can have something different than 0 or 1 , of course we all are too lazy to do it but there is absolutely no paradox because any computer could make that math easily ....... ggwp

I'm a little confused regarding your comment that the probability of getting any particular result out of a set of results holds in the case of a countable, or actual, infinite.
If we had a random number generator that was going to generate one natural number out of all the natural numbers, then the probability that it would generate any particular natural number, lets say the number 7, would be 1/Aleph_0. But 1/Aleph_0 is 0. There would be a 0% probability that the number 7 would be generated by this random number generator.
But this holds true for every natural number. For any natural number "n" there would be a 0% probability that number would be selected.
But if the probability of every number being selected is 0%, then the total probability of getting a number is 0% as well.
But, of course, this number generator is going to generate a number, so the probability of getting a number needs to be 100%.
So we arrive at a contradiction.

When a girl tells me i have 0 chance of sleeping with her i just show her this video.

what if it lands on the rim

I wanted to do this for a physics lab once and got 0 support from the teacher because it wasnt part of the lesson

So the average of 0 and 1 is .5 or 50% which of course is the probability of a coin coming up heads.

I understand what you present in this video, but really the whole thing is just "how to avoid a paradox" that doesn't even really exist. The probability isn't 0, it's infinitely near 0 (and has such adding every single scenario (infinite) does make one). That's why maths contoured it to be able to use it in calculations. At least that's how I see it.

50% of the time it works every time. Simple probabilities

Probability of zero does mean impossible. Random real numbers cannot actually be produced or observed.

The process of doing so would involve generating digits in some way, and you will never get to the point where you're "finished" and have an actual random real number.

Real numbers are a limit.

The probability of me understanding this video is 0

to ma sens dzieki

This video is the hard way of saying rounding to 0 is a thing

Technically there is no such thing as zero.

Wat? Of course you can add infinite values above zero with a finite value

Man! It has bothered me for sooo long now. But saying that there is an whole different axiom underlying for continuems makes it easier to digest.

I have no clue what he means by "probability of 0" or why he would even think something with a probability of 0 can be "possible". Can someone decode the language?

I just realised - this notion of probability 0 but area under graph 1 bears some resemblance to the Dirac delta function, which is 0 everywhere except at x=0, where it is “equal” to “∞” such that the integral from ±∞ of δ(x) is 1.

no

Not zero probability. Infinitesimal probability. The sum of the infinitesimal probabilities is 1.

So 1/∞ isn't zero, otherwise the probability would be zero if you added up all the probabilities. Or if it is zero, there is something wrong with how we calculate probabilities.

I disagree with the name of the video. The probability, so far demonstrated is zero, within experimental error and accepting that there is a probability distribution associated with the accuracy of that zero.....but that DOES NOT equate to the event having a probability of zero. Because a probability of zero really DOES mean 'will not happen'.