What is the difference between probability and possibility?

They answer different questions. Possibility asks, “Could this outcome happen?” Probability asks, “How likely is it, according to this model?” An outcome can be possible without being likely.

For example, suppose a model describes one roll of a fair six-sided die. Rolling a 6 is possible, and under the fair-die assumption its probability is 1 out of 6. The number describes likelihood under the model; it does not determine what the next roll must be. A probability model includes a set of possible outcomes, and assigns probabilities from 0 for an impossible event to 1 for a certain one. [S1]

Not always without clarifying what “possible” means. In ordinary conversation, “possible” can mean that we can imagine an outcome or have not ruled it out. In the probability model described here, an event assigned probability 0 is impossible within that model. So first ask which outcomes the model includes and how it assigns probabilities. The model’s answer depends on its definitions and assumptions; it does not settle every broader meaning of “could happen.” [S1]

For a small, finite example, list the outcomes the model allows and then look at their assigned probabilities. Don’t infer that an outcome is included merely because someone mentions it.

Name the outcome, then separate whether it can occur from how likely the model says it is. For example: “A 6 is possible on this die roll, but under the fair-die model its probability is 1/6. It could still be a different result on this particular roll.” That is not a contradiction: “possible” means the outcome is allowed; “unlikely” describes its likelihood compared with alternatives.

Be careful to say “under the model.” The equal-outcomes counting rule applies when outcomes are equally likely; don’t use it if equal likelihood has not been established. [S1] This example illustrates the distinction; it does not prove that a particular die is fair.

Ask what event the number describes, which outcomes the model includes, and what assumptions it relies on. A probability is not proof that a specific outcome will occur. For instance, a probability of 1/6 in the die example does not mean that every six rolls must contain exactly one 6; it describes likelihood within the stated model, not a guaranteed schedule of results.

A useful explanation you can adapt is: “The outcome [outcome] is [possible/impossible] within [stated situation]. Under the model that assumes [assumptions], its probability is [number]. That number describes likelihood; it does not guarantee the result of one particular trial.” If you cannot state the model or its assumptions, present the number as uncertain or incomplete rather than as a bare fact.