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.