01.05 · Lecture
Availability Is Multiplication
State the probability axioms and say precisely when two events are independent - the condition every availability calculation in this course quietly assumes.
Availability multiplication is valid only when the component events are independent. The probability axioms define legal probabilities, certain outcomes, and addition for mutually exclusive events; independence is the extra condition that lets you multiply. Shared databases, nodes, caches, regions, or control planes can make attractive uptime arithmetic wrong.
What this lesson answers
- when can I multiply service availability numbers
- what does independence mean in availability calculations
- why redundant replicas do not guarantee independent failure
Notes
Availability Is Multiplication — Availability calculations exist to predict whether a system is reachable despite failures; without the probability rule only under independence, multiplying component uptimes produces false reliability numbers.
Key Concepts: - Probability axiom 1: for any event , , so availability is . - Probability axiom 2: the sample space is certain, , meaning one of all possible outcomes must occur.
Common questions
- When is it correct to multiply availability figures?
- It is correct when the events are independent: knowing one component is up or down does not change the probability that the other is up. In system terms, that means no shared failure source relevant to the calculation, such as the same node, primary database, cache, DNS dependency, region, or control-plane path.
- Why does redundancy sometimes fail to improve availability as expected?
- Redundancy helps only when the redundant paths can fail separately. If every replica still depends on the same primary database, regional API, deployment mechanism, or network configuration, then one fault can remove all of them. The arithmetic for independent replicas then overstates the real availability of the system.
- What is the practical difference between disjoint and independent events?
- Disjoint events cannot happen together, so their probabilities can be added for an either-or outcome. Independent events can happen together, but one happening does not change the probability of the other. Availability calculations usually need independence for multiplication, not disjointness, because components may be up at the same time.
Short definition: what is Availability Is Multiplication?