At my previous work, I was collating somewhat random unconfirmed animal sightings. I also had a separate database of animal occurrence probabilities (species distribution maps). I'm not a statistician but that sounded like a clear job for Bayes theorem: given a sighting and the overall probability of that sighting in that area (species distribution map), and some other assumptions about the noise of the sighting, what is the probability that the sighting actually included that species?

Claude asked me three questions and then wrote a beautiful Python implementation that queries the map and spits out a table of adjusted probabilities. Felt immensely powerful - I can do this 'on my own' now, I don't need to wait to find the right people or learn the right thing first.