Multiplicative Rule

The multiplicative rule says that for independent events, the probability of all occurring is the product of their individual probabilities. If each step in a chain has 90% reliability, a ten-step chain has 0.9^10 ≈ 35% reliability. The intuition-breaking insight: small individual risks multiply into large systemic risk. In business, a launch that depends on five things each "probably fine" at 80% has a combined probability of roughly 33%. The rule forces you to count dependencies, not just evaluate each step in isolation. Reducing the number of must-go-right steps — or raising each step's probability — is the lever.

List every must-go-right step. Estimate each probability. Multiply them. If the product is uncomfortably low, either reduce the number of steps or raise the probability of the weakest ones. The weakest link has the most leverage. Use this to reality-check plans that "should work" on paper.

The multiplicative rule says the probability of all independent steps succeeding is the product of their individual probabilities. Small per-step risks compound into large systemic risk. Simplify plans, raise the weakest probabilities, and multiply before you commit.