Doubt, possibility, unlikelihood

il est possible que

Subjunctive

Example

Il est possible qu'il pleuve demain.

Do not write

Il est possible qu'il pleuvra demain.

Why

A CLASSIC TRAP, and it must be compared with il est probable que, which takes the indicative. Possibility leaves the fact hanging, hence the subjunctive; probability presents it as expected, hence the indicative.

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Doubt, possibility, unlikelihood