Ethereum rollups at Stage 1 can fail if the proof system fails and three or more security council members are unavailable to override the failure, or if six or more council members are compromised and force an incorrect decision

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We can do this with binomial distributions: If each security council member has an independent 10% chance of breaking, then the chance that at least 4 of 7 will break is Thus, a stage 0 rollup has a fixed 0.2728% chance of failing. A stage 1 rollup can fail if either the proof system fails and the security council gets >= 3 failures so it can't override (probability multiplied by the proof system failure rate), or if the security council gets 6+ failures and can force an incorrect answer by itself (fixed probability) The chance that a stage 2 rollup will break is just equal to the probability that the proof system fails