How to calculate probability of specific node failing in a network

The failure rate is going to be based on what it taking place on the Node. If you are running SAN storage as an example, and you have different clusters of storage used for different things ie: Exchange vs SQL vs VMware vs Print/File hosts. You can bet the Exchange and SQL storage is going to have a higher failure rate due to the IO taking place on the systems.

When you talk about failure, are you looking for total system crash, hardware failure, network failure or combination of all? What you need to look at is the writes taking place to disk. Lower writes/traffic to the system will mean less wear and tear on the system and a lower failure rate.

You haven't defined failure or fault. And if this is an exercise in computing failure probability in a (somewhat) redundant system, what are the failure rates of the individual components?

Thank you for your replies...To be honest I havent thought about particular failures. Let me explain what I am thinking (btw this is not an assignment or something, it's totally out of interest).
Say we have 10 clusters.
Each cluster has the following: 2 hubs connected to each other and each hub is connected to 3 nodes (imagine all of that in a tree structure apart from the clusters for which we can have a main bus that connects them or something, havent thought of that yet).
Those two hubs in each cluster have one node that we need to keep working as much as possible ie with higher probability than others and 5 nodes that we dont care that much (the important node is connected to both hubs). That is: Hub 1 has 1 imp(for important) node and 2 nimp(for not important). Hub 2 has 3 nimp. Same for the other clusters.

What I am trying to do is calculate the probability of 1 imp node failing using the structure above. My initial idea was to write down just one cluster as a tree (that is, no links on components of same level or from the 1 imp node to the other hub) and calculate the probability of the 1 imp node failing which I guess is simple: 10 clusters, so prob of 1 cluster failing equals 1/10. in the cluster we have 2 hubs so prob of the one that contains the imp node failing is 1/2. so far 1/10*1/2.
and we have 3 nodes connected to the hub so prob of the imp node failing is 1/3. so totally 1/10*1/2*1/3 = 1.6%

As you can see my calculations were in the simplest scenarion possible without taking into account other factors like damaged devices, cable quality etc etc. I just want to calculate in some similar way the probability of 1 imp node failing in the structure I described above which I guess cant be called a tree now, looks more like a graph?

I hope my description was ok, sorry i am not a native speaker. pls ask for any querries. as i said i am new in networks and try to figure out how we can assure continuous service(as much as possible) to a specific node compared to others.

The probability is 1 - it will eventually fail, although it may take hundreds or thousands of years. I suspect you're interested in something like Mean Time Between Failures (MTBF). If that's the case, you'll need failure rate data for the components of the system.

The probability of 1/10 that you came up with is relevant if the question is:
Given 10 clusters with equal failure rates, what is the probability that when a cluster failure occurs, it is this specific cluster that fails?

yes that is the one I calculated , that was my intention you are right.

Thanks for the explanation to my question, it made thinks somewhat more clear for me!