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.
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.