Years ago on hackernews I saw a link about probability describing a statistical technique that one could use to answer a question about if a specific type of event was becoming more common or not. Maybe related to the birthday paradox? The gist that I remember is that sometimes a rare event will seem to be happening more often, when in reality there is some cognitive bias that makes it non-intuitive to make that decision without running the numbers. I think it was a blog post that went through a few different examples, and maybe only one of them was actually happening more often.

If the events are independent, you could use a binomial distribution. Not sure if you can consider these kinds of events to be independent, though.