In most applications I think Bayesian reasoning is not that useful in everyday life, but I do think it would be pretty effective a strategy for like, planning the perfect murder. When people talk about committing the perfect murder they always come up with all this elaborate stuff like "oh we're gonna dissolve the body, blah blah", but the thing is, a ton of murderers don't get caught, and there are widely available statistics on every conceivable type of murder and just how likely it is to get solved. By going through all these statistics, you could not only plot a murder with a very low probability of getting caught, but get a quantitative estimate of just how likely you are to get caught and rationally weigh that against the expected pay off.
Someone should write a ratfic whodunit about this.