<p>In experimental practice, especially where the human factor plays an important role, we are faced with the need to analyze phenomena burdened with two types of uncertainty simultaneously: randomness and a lack of precision. While probability theory deals with randomness, and we cope with imprecision using the theory of fuzzy sets, combining both these descriptions is neither straightforward nor simple. Even seemingly simple tasks, such as calculating the probability of an event for a fuzzy random variable, are not obvious. In this contribution, we propose a method of calculating probabilities related to the so-called LR fuzzy random variables. Besides indicating the general method, we show how, in situations where it is difficult to obtain an analytical solution, it is possible to determine the desired probability using numerical methods, referring to the Monte Carlo simulations. The considered approach is illustrated with examples, also based on the real-life dataset.</p>