Okay, so probability...
The frequency of the event divided by the total number of possible events...
So, the probability of a coin landing heads up after being tossed on the floor, is 1/2..
Or 50%.. but there are three possibilities here... Heads, tails, or... Landing on it's edge... So why isn't the probability actually 33% that the coin will be heads?
Edge is excluded from possible event as it is not wanted to accept. if anyone want to accept the edge as ppssible event then edge must prepared as like as head or tail.
If YOU want to do that, you go right ahead.
WTF!
My research shows that your initial premise is faulty. Probability is the ratio of equally likely events.
"The probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes, assuming each outcome is equally likely to occur.". Since we know the chances of a coin landing on its edge isn't close to whether it lands on either side you can't throw that in and try to make it equal.
Ah... I didn't know about the condition of the events being equally likely. Thanks
Isn't it actually IMPOSSIBLE?
@Storm1752 of course not. You have never dropped a coin and had it stay on its edge? I've seen that happen several times.
The purpose of a coin toss is to have one of two outcomes, the third "possible" outcome is irrelevant to the purposes of a coin toss and so is generally disregarded, under such circumstances.
As a purely mathematical or statistical experiment then yes it should be counted.
No, because it's IMPOSSIBLE, so can be statistically ignored.
@Storm1752 Highly improbable, but not impossible
It always lands on its edge. It just doesn't stay there.
Ahhhh !!! Thinking out of the box !!! I like this approach !!!! Strictly speaking you are correct
@IamNobody yes. I have a problem thinking when I'm in the Box.
It's also possible that the sun explodes while the coin is mid air, but we don't include that either.
Why would you make such a ridiculous comment? I've seen a coin land and remain on its edge several times, therefore it is not beyond the realm of possibility, though statistically insignificant.
It's possible that gravity may vanish out of the blue and the coin stay floating, shall the probability be 25% then? Of course not, the possibility for gravity to vanish is null for practical purposes and the possibility for the coin to land vertical is very close to null.... therefore, 50 50 is the more accurate ball park prediction.
No, it's not possible for gravity to vanish.. do you also think it's possible that God exists? Please... Think logically...
@Cutiebeauty I was trying to make a case on possibilities with low probability but I see that I have failed. No problem. Talk to the expert that really knows how this work. Talk to a coin. Tosse it and keep carefull record of the results. As the number of events increase, you will see how the 50 50 pattern emerges. If you happen to have an event where the coin land vertical then you will have enough data for tales, head and vertical to see why it cannot be 33%, which is your question. The coin, the experiment and the numbers will give you the answer.
It IS null.
That's not part of the hypothetical.
Well, if you count the odds like that, then what about the chance that the coin suddenly deforms to have two heads on either face? or what if the coin suddenly turns into a flat washer? Or a ball? or every atom suddenly and spontaneously melts and turns into a pile of molten metal before re-solidifying into a metal figure of Ceasar? Of course it could also be a statue of George Washington, but it is just as likely to be a statue of Lincoln riding a T-rex.
Therefore the odds that the coin lands on heads are infinitesimal, because there are infinite possibilities for how the coin could end up after landing on the floor.
Okay.. if you don't have an opinion, just say so...
@Cutiebeauty I'm just showing how ridiculous it would be to count the odds like that through the use of satire. If you want to count the odds like that, saying that there is a 33% chance the coin lands on it's side is wrong because there are still more possibilities, like all the ridiculous ones I listed. That would be the percentage of possible outcomes, and is more or less a totally irrelevant way to define finite sums, because you could just say "there are 3 possible outcomes"
We say the odds are 50% that a coin lands on heads not because there are only two options, but because all the other possibilities are incredibly unlikely.
@Happy_Killbot unlike your possibilities, a coin landing on it's edge is actually possible... So I'm asking why isn't this taken into account...?
@Cutiebeauty All the things I said are possible, just incredibly unlikely. For example, some coins have been accidentally minted with two of the same side. It's also possible that the coin melts if it encounters a large heat source, for example it could fall into a fire. These things all have a non zero probability, same with the coin landing on it's edge. For a coin to land like that requires very specific circumstances, and if we can change those circumstances you can make the coin land however you want. You could flip the coin into a machined funnel that would make the chance it lands on it's edge nearly 100%. It's about the usefulness of that definition.
Because the government paid for the test.
Test? What test?
@azzow2 I'm not looking at a link.. tell me yourself what test you're talking about.. I want a discussion here...
@Cutiebeauty In the late 1960` and early 1970s, the government funded some scientific test one of which was to see how a frisbee flies, remote viewing, probability test, etc.. I have no idea what the results were or why they wasted so much tax dollar to find the results.
I think we look at odds in a way that makes a probability more probable, either positively or negatively depending on if we are an optimist or a pessimist. And we tend to eliminate the least possible of outcomes because it is one less thing to think about. As humans we hate complications.
Huh? Mathematics is one hundred percent objective. . I don't understand your reply...
@Cutiebeauty I'm answering based on a human being not running their life according to mathematical certainty. Even actuarial charts are not written in stone. If the world ran on pure mathematical standards it would be a different world and maybe not for the better. Think about Dr Spock from Star Trek; that isn't who we are. Things just may be black and white but humans rarely look at it that way. And anyway the way you raised your question mathematically was flawed so there really isn't any way to have discussion because you don't seem to want to look at it any way but in the way you have decided to look at it. Just as a closing remark, I'm not trying to argue or change your mind I'm just trying to tell you what I think but you have already told me you do not understand my more psychological answer because I think people are not computers
@AmelieMatisse please explain how my question was mathematically flawed when you actually approached my question from a psychological perspective..
@Cutiebeauty Because when you asked the question of shouldn't it be 33.33% for heads, tails, edge. There is no chance of equal probability of the coin landing on those 3 surfaces equally. So that argument is not arguable. The coin landing on its edge may have a less than 1% chance of that happening at all so it can't be viewed equally for those 3 options because it would be squewed from the start.
Maybe the problem is using coins or anything thrown because you have to factor in the human doing the throwing as they will not throw the same way every single throw.
How I choose to approach and answer your question has little to do with the mathematical nature of how you posed the question. I'm a right brain thinker so my take is different than a left brain thinker. That's all I'm trying to say.
Because landing on its edge is not nearly as probable as it landing on a side. The actual probabilities are more like 49.99999999999 for heads, 49.99999999999 for tails, and 0.00000000002 for edge. And that's being generous for landing on edge.
Yeah, I get that... I'm actually talking about the way we go about defining the odds... You get what I'm saying?
We don't flip a coin thousands of times and then state the results like in many scientific experiments .. we constructed a definition..
@Cutiebeauty The odds are so negligible for it landing on itβs side that itβs not worth giving them.
@Cutiebeauty the odds can be calculated using surface area ratios, friction, velocity, and momentum.
Although there have been studies where they do coin flip after coin flip, and i don't think it ever hits a true 50/50. But i also don't think there were many edge landings, either.
@Marionville ok, you're approaching my question with foreknowledge of the results.. I'm considering the actual system of calculating the probability of the event.. the event divided by all possible outcomes. .
@1of5 okay, good answer. . But all that isn't included in the calculation of the probability...
@1of5 btw, you're very intelligent...
@Cutiebeauty thanks. I mask it well by being a jerk.
I did forget to add that the initial side up also influences the outcome.
This vid is pretty cool, btw.
[khanacademy.org]
@1of5 initial side up? Would that work with the new York daily number or any other lottery?
@Cutiebeauty don't I wish