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.
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.
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.
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:
any number less than 5 is rolled
a 5 is rolled
a 6 is rolled
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:
any number less than 5 is rolled: 4/6 (or 2/3 or 0.666… or 66.666…%)
a 5 is rolled (1/6 or 0.1666… or 16.666…%)
a 6 is rolled (1/6 or 0.1666… or 16.666…%)
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 2100 possibilities, but we will examine only 2 for this matter:
you will get 100 times tails
you will get as many tails as heads
Let’s say the cutoff point is 0.01, i.e. 1%.
This would make the first possibility improbable, as 1/(2100) is far lower than 0.01.
The second possibility is 0.5, which is greater than 0.01, and therefore probable.
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.
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.
How would you distinguish the 3 terms? Are probabillities and plausibillities roughly analagous)
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.
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 2100 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/(2100) is far lower than 0.01. The second possibility is 0.5, which is greater than 0.01, and therefore probable.
Thank you.