No Stupid Questions

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.

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

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.

maybe all the stats have eroded any intuition I had for these words

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 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.

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.

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.