GRAMMAR DETAIL

〜ものか

there is no way

Uses a rhetorical question to emphatically reject a possibility or express a firm refusal to act.

Examples

あんな不公平な条件を受け入れるものか。

There is no way I would accept such unfair terms.

こんな失礼な頼みを聞くものか。

There is no way I would comply with such a rude request.

Structure: ものか after a verb uses a question form to emphatically deny a possibility or firmly refuse an action.
Basic usage: あんな不公平な条件を受け入れるものか。 is a strong refusal to accept such unfair terms.

A rhetorical question rather than a request for an answer
- こんな頼みを聞くものか does not ask uncertainly whether to comply; it rhetorically refuses. Rendering it as a neutral request for confirmation loses the force of that refusal.
Refusal versus prediction
- In the current example, 受け入れるものか expresses the speaker's unwillingness to accept. It conveys stronger emotion and refusal than a mere prediction of low likelihood.