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があるだろうか

could there be?

→ が
phrase Rare #30,668
could there be? Often used in rhetorical questions to suggest that something is unlikely or impossible.
JA: これ以上いい方法があるだろうか。
EN: Could there be a better way than this?

今彼を説得して何か益があるだろうか。

Would there be any point in trying to persuade him now?

失明すること以上に大きな不幸があるだろうか。

Is there any greater misfortune than going blind?

彼がそんなことを言ったはずがあるだろうか。

There's no way he would have said such a thing.

近い将来、地震があるだろうか。

Will there be an earthquake in the near future?