Yeah, you can use Binomial distribution. If you're trying to find the probability of finding exactly one shiny after n encounters, it would work, however the way Orange stated is a lot easier, and gives you the same answer. Having said that, you can do more cool things with Binomial distribution, i.e if you want to find the probability of exactly 3 shiny encounters, or at least 4 shiny encounters etc after n encounters in total. Does that answer your question?