A file is split into $M$ parts and stored at $N$ nodes: the 1st part (of the first copy of the file) stored on node $1$, the second on node $2$ and so on, wrapping circularly. Each part of file has $K$ copies stored on these nodes (e.g. the same as the first copy but rotating the tuple of nodes to one node for the second copy, rotating (wrapping circularly) to two nodes for the third part, etc.)
The probability of node failure is $q$. What is the probability that the entire file can be restored (we assume node failure erases all the file parts stored on it).
My attempt to solve:
Probability of a copy of a shard to be damaged: $q^{1 / K}$.
Probability of a shard to be damaged: $q^{N / K}$.
Probability that a file goes well: $1 - (1 - q)^{N / K}$.
Also, can you propose more reliable strategy of storage on $N$ nodes than mine?