Large language models (LLMs) have demonstrated strong performance across a wide range of reasoning tasks, yet their understanding of joint and conditional probability distributions remains largely unexplored. In this work, we present a comprehensive evaluation of LLMs’ ability to reason about discrete joint and conditional probability distributions involving multiple random variables. Given observations drawn from a distribution, we evaluate models on three carefully designed tasks—mode identification, maximum likelihood estimation, and sample generation—which together capture fundamental skills required for probabilistic reasoning. Our study reveals both capabilities and limitations of current LLMs. In sample generation task, some models produce empirical distributions that closely match the target distribution despite exhibiting limited sample independence. We further observe that model performance is highly sensitive to representation: replacing explicit frequency information with raw samples leads to large accuracy drops, and even minor changes to outcome labels can further degrade performance. Together, these findings provide new insights into how LLMs reason about discrete joint and conditional probability distributions and highlight their strengths and limitations in certain probabilistic reasoning settings.

Fact-checking tabular data is essential for ensuring the accuracy of structured information in domains such as journalism, finance, and scientific research. However, existing methods often rely on black-box models with opaque reasoning. We introduce RePanda, a structured fact verification approach that translates claims into executable pandas queries, enabling interpretable and verifiable reasoning.To train RePanda, we construct PanTabFact, a structured dataset derived from TabFact, where claims are paired with executable queries generated using DeepSeek-Chat and refined through automated error correction. Fine-tuning DeepSeek-coder-7B-instruct-v1.5 on PanTabFact, RePanda achieves 84.09% accuracy on TabFact. To assess Out-of-Distribution (OOD) generalization, we create a dataset named WikiFact from WikiTableQuestions by transforming question-answer pairs into factual claims. Without additional fine-tuning, RePanda achieves 84.72% accuracy on WikiFact, significantly outperforming all other baselines and demonstrating strong OOD robustness. PanTabFact is publically available on HuggingFace at datasets/AtoosaChegini/PanTabFact.Beyond fact verification, RePanda extends to tabular question answering by generating executable queries that retrieve precise answers. To support this, we introduce PanWiki, a dataset mapping WikiTableQuestions to pandas queries. Fine-tuning on PanWiki, RePanda achieves 75.1% accuracy in direct answer retrieval. These results highlight the effectiveness of structured execution-based reasoning for tabular verification and question answering.