What are the differences between 1) probabillities, 2) possibillities, and 3) plausabillities?
from cheese_greater@lemmy.world to nostupidquestions@lemmy.world on 30 Jun 17:35
https://lemmy.world/post/32279518
from cheese_greater@lemmy.world to nostupidquestions@lemmy.world on 30 Jun 17:35
https://lemmy.world/post/32279518
#nostupidquestions
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If you flip a coin, the result has two possibilities: It may show either the obverse side (head) or the reverse (tails). These possibilities have equal probability (“50:50”), i.e. in 100 times the coin is flipped, statistically both sides are shown 50 times.
How would you distinguish the 3 terms? Are probabillities and plausibillities roughly analagous)
Possibilities are all possible outcomes of a certain scenario. With the example of a coin toss, it’s heads or tails. However, these are dependent on your definition of what you want to observe. For example, at a dice roll, you could define the possibilities as:
Probabilities are attached to possibilities. They define how likely an outcome is. For example, in an ideal coin toss heads and tails have a probabilitiy of 0.5 (or 50%) each.
With my 2nd example, the probabilities would be:
All probabilities must add up to 1.0 (or 100%), otherwise your possibilities overlap, which is generally not something you want.
Plausibility is a bit more tricky, as it also depends on your definition, namely a cutoff point. You could see the cutoff point as a limit of how much you want to risk. I’ll only examine the example for the coin toss for that. Say you will toss a coin 100 times. This would mean there are 2^100^ possibilities, but we will examine only 2 for this matter:
Let’s say the cutoff point is 0.01, i.e. 1%. This would make the first possibility improbable, as 1/(2^100^) is far lower than 0.01. The second possibility is 0.5, which is greater than 0.01, and therefore probable.
Thank you.
A common dice has 6 possible outcomes. Unless it’s a special D6, it’s impossible to get a zero or some other value outside the usual range of 1-6.
Normally, each side has a probability of 1/6. If it’s a loaded dice, one value will have a higher probability, while the other sides will have a lower probability.
Let’s say you have two dice, you roll them, and hope to get 6 on both of them. It’s possible to get that on the first try, but it’s much more plausible that you have to roll them many times before that happens.
But, it is plausible you didn't flip 50:50 since the 50:50 is on average.
Exactly, 50:50 is statistically the most likely scenario (7.96%), while e.g. 51:49 being only slightly less likely (7.80 %). A strongly biased distribution as e.g. 60:40 only has a small probability of 1 %, but is not impossible.
Probabilities will likely happen.
Possibilities could happen if chances go right.
Plausibilities could, within reason, happen, but are not necessarily likely.
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They’re not just different ranges of probability.
Probable = likely to happen
Possible = able to happen
Plausible = able or likely to happen according to reasonable inference
Possibility: it can technically happen
Probability: statistically significant likelihood of happening
Plausibility: a possibility that passes the laugh test
Actually a great heuristic, thanks!
Very plausible response
My understanding would be:
Probabilities: Chance of a certain outcome happening. E.g. Outcome A has a 70% chance B a 20% and C 10%
Possibilities: what outcome scenarios exist. E.g. there exist 3 (A B C). Those Possibilities might have a probability associated with them
Plausibility: looks at the degree of truth of a statement. So if it logically makes sense and is the correct answer/is what happened. You might make a judgement of the plausibility of a possibility based on the probability of it happening. Say if something has two outcomes one with a 99% chance and the other 1% then that might be the more plausible one. Or if it has no chance, then it might be implausible
Edit: since someone mentioned the example of a coin toss.
Head and tails have a probability of 50% each (for the sake of simplicity I assume it won’t land standing up)
A coin toss has two possible outcomes (possibilities). Head and tails.
Someone says he flipped a coin and got head 1000 times in a row. That’s not plausible with a fair coin because of the low chance of it actually happening (even if there is a indefinitely small chance). As a result you might assume he is either lying or the coin is weighted for that outcome.
There is also the extreme implausibility with a <1% probability that it will land on its edge but still more possible than 1000 heads in a row.
1 in 6000 chance for an American nickel, which has a thicker side than most. Just for others sake. I felt it was far less than just <1% and had to find out.
Probability is a numeric value between: 0 and 1 of how likely an event is going to happen. Depending on the definition, I would say that possibilities and plausabilities are both events with a nonzero probability. Colloquially, possibilities are more likely than plausabilities I guess. Source: two thirds of a stats phd and C2 level english skills lol
when people say its plausible tho, I feel like that means its a bit more likely or they entertain the chance of it happening or being correct more than a mere possibillity tho
maybe all the stats have eroded any intuition I had for these words
Plausible is more like conceivable.
It’s possible that when I slam my hand on the table, it will go through the table, but it’s not plausible. We can’t imagine it actually happening, even though we know it can.
Coin toss:
Probabilities - The mathematically determined chance that something will happen given a specific scenario.
Possibilities - The set off all things with a >0% chance of happening given a specific scenario.
Plausibility - The outcomes of a specific scenario, that when presented to a reasonable person, that person would determine that they are possible.