4. Katya and Pasha ask each other four tricky questions and answer them without thinking, randomly. The probability that Katya will lie to a question asked by Pasha is $\frac{1}{3}$, regardless of the question number. Pasha gives a truthful answer to Katya's question with a probability of $\frac{3}{5}$, independently of the question order. After the dialogue, it turned out that Pasha gave two more truthful answers than Katya. What is the probability that this could happen?
Answer: $\frac{48}{625}$.