product of experts & mixture model

ref: http://www.scholarpedia.org/article/Product_of_experts

One can qualitatively understand the difference between mixtures and products by observing that a mixture distribution can have high probability for event 

x  when only a single expert assigns high probability to that event. In contrast, a product can only have high probability for an event  x  when no expert assigns an especially low probability to that event. Hence, metaphorically speaking, a single expert in a mixture has the power to pass a bill while a single expert in a product has the power to veto it.