We use puede que followed by the Modo subjuntivo to express probability or possibility (It is possible that..., I may ..., You may..., It may...)
Expressing probability/possibility in the present or future in Spanish
If the probability/possibility is related to a present or future situation, you will find El Presente de Subjuntivo after puede que.
See and listen to the following examples:
Possibility in the present
Possibility in the future
Expressing probability/possibility in the past in Spanish
If the probability is related to a past situation, the verb will be in one of two past subjunctives.
See and listen to the folowing examples:
Both El Pretérito Imperfecto Subjuntivo and El Pretérito Perfecto Subjuntivo express a possibility in the past. Using one or the other just depends on whether you want to convey the completion of the action (use the perfect subjunctive, e.g., haya ido, haya comprado...) or a more generic action in the past (use the imperfect subjunctive, e.g., fuera, comprara, hiciese...)
See also Using the subjunctive or the indicative after tal vez and quizás to express doubt in Spanish
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