What can you do with Probability and Statistics?

1) You can realize that almost any statistic you see in the news is crap such that it is almost guaranteed to be misinterpreted.

2) If you really dig in you can internalize some of the mechanisms of statistics and use them to build mental models of probability in your head and better predict outcomes in a sense that might help you make better decisions to begin with.

3) You will better understand how the world around you operates and what the risks are in systems like the stock market. It won't make you a quant but it will help provide some intuition about these systems.

A good community online that I recommend with a grain of salt is lesswrong.com. They try to apply bayesian probability theory to daily life among other things along that train of thought. I say a grain of salt because they are almost worshipers of that model of the world even though it is not the only way to look at the world.

 

Statistical Mechanics and Quantum Mechanics both make use of probability theory. Statistical mechanics make use of more advanced probability theory, as far as I know.

Statistics is hugely important to interpreting the results of an experiment. A measurement is pretty useless if you don't know the accuracy and error that come along with it.

And, in a first probability course you will likely learn about counting/combinatorics and just general distributions and those just come up a lot in all types of areas.