The possibility of considerably increasing the resolution of an extended image taken through a turbulent atmosphere by selecting random "lucky" diffraction limited exposures out of many normal-turbulence degraded-short exposures is experimentally explored. For an imaging aperture D, larger than the atmospheric spatial coherence length ro, the probability P of getting a diffraction limited short exposure image of a point source is found to be exp[-0.6(D/r0)2 ]. This result is in agreement with Fried's prediction. The angular isoplanatism is measured to be -X/ro. However, observed random wavefront tilts scramble the diffraction limited picture elements in an isoplanatic patch, thus complicating the probabilistic imaging method.