The double-slit experiment
This is the famous double-slit experiment. It is often used to explain the mysteries of quantum mechanics. A particle hits a screen with two slits or holes in it. If the experiment is repeated very often, then one can determine the probability for the detection of a particle in a certain direction. This probability is described by the wave function. Since each of the narrow slits is the origin of a spherical wave, there is an interference pattern behind the screen. In some directions, the contributions cancel out and the probability that particles are found in these directions is about zero.
This is the typical behavior expected from a wave phenomenon but it is paradoxical in the context of the particle interpretation. The paradox arises if we compare this with the single-slit experiment. If only one slit is open, the probability distribution behind the wall is roughly spherical. In some directions, the probability of finding the particle decreases, if we open both slits. According to classical considerations the opening of both slits would increase the possibilities for the particle to go behind the wall. Hence the probability of finding the particle behind the wall should be larger than in the single-slit situation for all directions!
"Visual Quantum Mechanics - Book One" contains an in-depth analysis of the double-slit experiment and its consequences.