Gemini

Dima and Zhenya are twin brothers. Not only do they look identical, but they also always sit together at the same desk in class. One always sits on the left, and the other sits on the right. Each claims to be Dima. Mr. Smith knows from experience that the boy sitting on the right tells a lie once out of $m$ times, while the one sitting on the left does so once out of $n$ times. However, what really interests Mr. Smith is: what is the probability that Zhenya is sitting on the left?

Since Mr. Smith is a teacher, it is only natural for him to ask for your help in solving this problem.