Explains why the availability of components in series is the product of their availabilities
A chain works only when every component works; if components fail independently, the probability that all work is the product of their availabilities (0.999 x 0.995 = 0.994); dependent failures need the conditional probability instead.
Can AI do this?
AI does this well Most of the tested AI models master this. 4 of 4 models in the current benchmark master it.
| Model | Tier | Probability of mastery | Status |
|---|---|---|---|
| gemini-4-argon | Flagship | 100% | Mastered |
| gemini-3.5-flash-lite | Low cost | 100% | Mastered |
| gpt-6-luna | Low cost | 100% | Mastered |
| claude-haiku-5-5 | Low cost | 99% | Mastered |
Mastered means a probability of at least 90% that the model has this knobit, estimated from its graded answers. “Not shown” means the answers do not settle it either way. How the models are tested.
What it looks like in practice
Expected result: Composed availability as the product of independent component availabilities, with the independence assumption stated
How it is assessed: Computes the availability of a chain of independent components as the product and states the independence it assumes
Related knobits
Builds on
Needed for
- O-631 Composes availability across a dependency chain
- O-652 Explains composing service levels from components
All knobits of Data storage and operations.
Source: Part B candidate of k12-dmbok for activity OV-11 (a need for school knowledge no knobit of the activity reached), accepted by Peep Küngas on 31 Oct 2026