4. Students $10^{2}$ calculated the arithmetic means $x_{n}=\left(a_{1}+a_{2}+\ldots+a_{n}\right) / n$ of the terms of the numerical sequence $a_{k}=(4 k-3) / 5, k=1,2, \ldots, n, n=1,2, \ldots, 13$. The probability of making an error in calculating $x_{n}$ is proportional to $n$, and the event "to make an error in calculating 13 means" is certain. When calculating $x_{11}$, the result $X_{11}=21 / 5$ was obtained. Find the probability that out of the calculations of $X_{10}, X_{11}$, and $X_{12}$, two will be correct.
Answer: $\frac{46}{169}$