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to be possible; to be conceivable; to be likely; to be probable
「有り得る」 has another reading with different meanings.
こんな偶然は有り得ないと思った。
I thought such a coincidence couldn't be possible.
技術の進歩で以前は有り得なかったことが実現した。
Advances in technology made possible things that were previously inconceivable.
ミスは誰にでも有り得ることだ。
Mistakes can happen to anyone.