I'm glad this is intuitive for you!

The reason I spotlighted labor-intensive methods is because this post is targeted at people who don't find this intuitive. I'd rather give them a method that can be extended to other situations with low risk (applying Bayes' Rule, imagining the world after receiving an update and calculating new probabilities) rather than identifying symmetries in the problems and using those to quickly get answers.

The rest of the sequence uses this as background, but probability calculations play a secondary role. The techniques I'll discuss require a moderate level of comfort with probabilities, but not with probabilistic calculations- those can (and probably should) be offloaded to a calculator. The challenge is setting up the right problem, not solving a problem once you've set it up.