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

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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.

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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:

• 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/(2^100^) is far lower than 0.01. The second possibility is 0.5, which is greater than 0.01, and therefore probable.