Probability plays a critical role in making sense of quantum physics, but most science and engineering undergraduates have very little experience with the topic. A probabilistic interpretation of a physical system, even at a classical level, is often completely new to them, and the relevant fundamental concepts such as the probability distribution and probability density are rarely understood. To address these difficulties and to help students build a model of how to think about probability in physical systems, we have developed a set of hands-on tutorial activities appropriate for use in a modern physics course for engineers. We discuss some student difficulties with probability concepts and an instructional approach that uses a random picture metaphor and digital video technology.