Assumptions To construct the mixnet we sample $n$ nodes (without replacement) from the population of $N$ nodes. At most $M$ , where $M<N$, nodes in the population are adversarial. The number of adversarial nodes $m$ in the mixnet is random number from the hypergeometric probability distribution $P\left(m\vert N,n,M\right)=\frac{{n\choose m}{N-n\choose M-m}}{{N\choose M}}$ We have $L$ layers constructed from $n=\sum_{\mu=1}^L n_\mu$ nodes, where $n_\mu$ is the number of nodes in the layer $\mu$. The probability that the number of adversarial nodes in layer 1 is $m_1$, in layer 2 is $m_2$, etc., is given by the multivariate hypergeometric distribution $P\left(m_{1},\ldots, m_{L}\vert n_{1},\ldots,n_{L}; m\right)=\frac{\delta_{m;\sum_{\mu=1}^L m_{\mu}}\prod_{\mu=1}^L {n_\mu\choose m_\mu}}{{n\choose m}}$ From above follows the joint probability distribution $P\left(m_{1},\ldots, m_{L}\vert n_{1},\ldots,n_{L}\right)=\sum_{m=0}^nP\left(m_{1},\ldots, m_{L}\vert n_{1},\ldots,n_{L}; m\right)P\left(m\vert N,n,M\right)$ Failures “Anonymity failure” occurs in the mix network when at least one adversarial node is present in each layer thus allowing to form a path of compromised nodes.