Suppose $n$ vaiables $a_1$ ~ $a_n$ distributed over $[1,n]$. Without loss of generity, let $a_i =n- i+1$.
Suppose that each variable has a probability $p_e$ to be wrong, and the wrong value uniformly distributes over $[a_i-∝，a_i+∝]$ where $∝$ is far smaller than $n$.
If we take out $b$ largest variableswhere $b≥k$ and $b<<n$, the question is what the probability that $a_1$~$a_k$ are all in the set of $b$ variables?
