Abstract: Bootstrap Percolation is a cellular automaton with a very simple description: given a (random) initial configuration in which each vertex of the graph is either occupied or vacant, at each time step vacant vertices become occupied if they have at least a certain number of occupied neighbours. In its version with noise, occupied vertices have a small probability of becoming vacant. We focus on the case In which the underlying graph is “expanding”. In suitable, different regimes, we show that large clusters of either type –occupied or vacant-- occur with exponentially small probability. The techniques are elementary and rely on familiar ideas in probability theory, such as Large Deviations and the trade-off between energy and entropy. No prior knowledge is required. If time permits, we will also discuss implications for other Interacting Particle Systems, most notably Kinetically Constrained Models and Majority Vote Processes.