Predict: what is the end to end success rate of a 10-step agent task if each step succeeds with 90% probability?

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An agent pipeline has 10 sequential steps. Each step succeeds independently with probability 0.9. Assuming no recovery mechanism, what is the end to end probability that all 10 steps succeed?

Quick reference

TL;DR

Independent step successes multiply, so a 10-step agent at 0.9 per step ends at 0.9^10, which is about 0.349, roughly 35% end to end success.

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Easy to grasp

Imagine a relay race where ten runners each have to hand off a baton. Each runner drops the baton one time in ten, so each one succeeds nine times out of ten. You might guess the team usually finishes fine. But every single handoff has to work for the baton to cross the line. The chance the whole chain survives is nine-tenths multiplied by itself ten times, not nine-tenths once. That comes out to about one in three. So even though each runner looks reliable on their own, the team finishes cleanly only about a third of the time. Long agent chains feel the same pain: each tool call seems trustworthy, yet stacking ten of them turns a small per step error into a big end to end failure rate.

Key concepts

Cascading Failure Agent Reliability

Detailed answer & concept explanation

~8 min read

Everything you need to truly understand this topic: intuition, mechanics, step by step explanation, code, formulas, and worked example. Click to expand.

Everything you need to truly understand this topic: intuition, mechanics, step by step explanation, code, formulas, and worked example.

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Quick scan · 2–4 min

Everything important, quickly.

Set up the independent Bernoulli model, derive reliability as p to the N, compute 0.9 to the tenth as about 35%, then invert it to show the punishing per step bar, and close with how retries and correlation bend the real curve.

Real-world examples

Real products, models, and research that use this idea.

SWE-bench coding agents show this directly: resolving an issue needs many correct edits and test runs in a row, so a high per-action rate still yields a much lower full-task resolve rate.
Anthropic's guidance on building effective agents pushes for the fewest steps that work, precisely because each added tool call multiplies another sub-one factor into the success product.
LangGraph and OpenAI agent runtimes add retries and verification nodes so a single failed step re-rolls rather than killing the run, lifting the effective per step p above the raw value.
Frontier models like Claude Opus 4.7 and GPT-5.5 are judged on long horizon agentic benchmarks where per step gains compound, so a few points of per step reliability swing end to end scores sharply.

Interviewer follow-ups

What an interviewer would ask next. Try answering before peeking at the approach.

QIf you add one retry per step, how does the effective per step success rate and the end to end rate change?

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QHow does the curve change if step failures are positively correlated rather than independent?

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QGiven a target of 95% end to end over 20 steps, what per step reliability do you need?

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Don't say this

Red flags and common mistakes that signal junior thinking. Click to expand.

Most common mistake

Averaging the per step rate or quoting 0.9 as the answer. Independent successes multiply, so the end to end rate is 0.9 raised to the number of steps, not 0.9 itself.

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60-second cheat sheet

The night-before-the-interview bullets. Scan these on the way to the call.

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References

Primary sources. Skim if you want the original framing.