From BiblePortal Wikipedia

Vine's Expository Dictionary of NT Words [1]

A — 1: Δυνατός (Strong'S #1415 — Adjective — dunatos — doo-nat-os' )

"strong, mighty, powerful, able (to do)," in its neuter form signifies "possible,"  Matthew 19:26;  24:24;  26:39;  Mark 9:23;  10:27;  13:22;  14:35,36;  Luke 18:27;  Acts 2:24;  20:16 (27:39, in some mss.; dunamai, "to be able," in the most authentic, RV, "they could");   Romans 12:18;  Galatians 4:15 . See Able.

B — 1: Εἰμί (Strong'S #1510 — verb — eimi — i-mee' )

"to be," is used in the third person singular, impersonally, with the meaning "it is possible," negatively in  1—Corinthians 11:20 , RV, (AV, "it is not"), and  Hebrews 9:5 , "we cannot," lit., "it is not possible."

 Hebrews 10:4Impossible.

King James Dictionary [2]

POS'SIBLE, a. L. possibilis, from posse. See Power.

That may be or exist that may be now, or may happen or come to pass that may be done not contrary to the nature of things. It is possible that the Greeks and Turks may now be engaged in battle. It is possible that peace of Europe may continue a century. It is not physically possible that a stream should ascend a mountain, but it is possible that the Supreme Being may suspend a law of nature, that is, his usual course of proceeding. It is not possible that 2,3 should be 7, or that the same action should be morally right and morally wrong.

This word when pronounced with a certain emphasis, implies improbability. A thing is possible, but very improbable.

Webster's Dictionary [3]

(a.) Capable of existing or occurring, or of being conceived or thought of; able to happen; capable of being done; not contrary to the nature of things; - sometimes used to express extreme improbability; barely able to be, or to come to pass; as, possibly he is honest, as it is possible that Judas meant no wrong.