Every single drive in the datacenter typically has the same likelihood of failure (since they're usually the same make and model, and similar production runs), so the odds that a drive somewhere in a large data center is failing RIGHT NOW are in reality rather high.
The Big Mac ended up being a good example of this. The likelihood of having a memory error on a normal PC is low, because the likelihood of a single DIMM having a memory error is low.
Punch that up to the 22,000 or thereabouts DIMMs that populated the Big Mac cluster, and now you're looking at a very HIGH likelihood that a large-scale computation using the cluster will experience memory errors, and therefore produce invalid results -- which is why UVa ended up replacing the entire cluster with ECC-equipped machines in short order. Until they did that, researchers had to run simulations multiple times and compare results to make sure that their simulations weren't contaminated by memory errors.