Probabilistic/stochastic computations form the backbone of autonomous systems and classifiers. Recently, biomedical applications of probabilistic computing such as hyperdimensional computing for DNA sequencing, Bayesian networks for disease diagnosis, etc. have attracted significant attention owing to their high energy efficiency. Bayesian inference is  widely used for decision making based on independent (often conflicting) sources of information/evidence. A cascaded chain or tree structure of asynchronous circuit elements known as Muller C-Elements can effectively implement Bayesian inference. Such circuits utilize stochastic bit streams to encode input probabilities which enhances their robustness and fault tolerance. However, the CMOS implementation of Muller C-Element are bulky and energy hungry which restricts their widespread application in resource constrained IoT and mobile devices. To enable Bayesian inference based decision making in IoT devices such as UAVs, robots, space rovers, etc, for the first time, we propose a highly compact and energy-efficient implementation of Muller C-Element utilizing a single Ferroelectric FET. The proposed implementation exploits the unique drain-erase, program inhibit and drain inhibit characteristics of FeFETs to encode the output as the polarization state of the ferroelectric layer. Our extensive investigation utilizing an in-house developed experimentally calibrated compact model of FeFET reveals that the proposed C-Element consumes an ultra-low power of 1.07 fW. We also propose a novel read circuitry for realising a Bayesian inference engine by cascading a network of proposed FeFET based C-Elements for practical applications. Furthermore, for the first time, we analyze the impact of cross-correlation between the stochastic input bit streams on the accuracy of the C-Element based Bayesian inference implementations. For proof of concept demonstration, we utilize the proposed FeFET based Muller C-Element for performing breast cancer diagnosis utilizing Wisconsin data-set.