Large language models (LLMs) in financial applications fail most consequentially when they are confidently wrong. Hedged, uncertain answers invite scrutiny, whereas confident errors silently degrade downstream decisions without warning. We ask how reliably such confidently wrong answers, or confident hallucinations, can be detected from a model's internal activations, and whether those activations carry information beyond its output-level confidence signals. We train linear probes on the residual stream and evaluate them on two established numerical question-answering (QA) benchmarks built from real filings, FinQA and TAT-QA. Behavioral confidence is measured as the agreement among eight resampled answers to the same question, and probe effectiveness is compared against baselines, such as token log-probabilities and the model's own True/False self-assessment of its answer. Our findings show that among confident answers, those for which all eight resamples agree, 15-23% are wrong on FinQA. There the probes have a significant advantage over output-level baselines in detecting hallucinations, holding 0.68-0.77 AUROC while the best baselines fall to 0.55-0.63, across Qwen3-8B, Llama-3.1-8B, and Gemma-2-9B. Our results suggest that probing can be a cost-effective triage mechanism for routing LLM answers to human review and quality control procedures in high-stakes financial applications. Code and data are available at https://github.com/richardzhewang/confidently-wrong.

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