Same topic, related formats. Practice these next.
You want an agent to complete a 10-step task with at least 90% end to end success rate. All steps are independent. What minimum per-step accuracy p must each step achieve to meet this target?
End-to-end success is p^N for independent steps. To clear 90% over 10 steps you need the tenth root of 0.9, about 98.9% per step.
Imagine a relay race where 10 runners each have to pass a baton without dropping it. The team finishes cleanly only if every single handoff works. If each runner is 90% reliable, that sounds great, but the chance all ten succeed is 0.9 multiplied by itself ten times, which is only about 35%. To get the whole team to a 90% finish rate, each handoff has to be almost perfect. Working backwards, each runner needs to succeed about 99 times out of 100. The lesson is that long chains punish small per-step mistakes brutally, because the errors multiply instead of adding. That is why people prefer fewer, more reliable steps over many shaky ones.
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.
Everything important, quickly.
State that independent step successes multiply, write reliability as p^N, invert to p = T^(1/N), compute 0.9^(1/10) ≈ 0.9895, then explain the reliability budget inversion and why step count is the dominant design lever before noting where independence breaks.
Real products, models, and research that use this idea.
What an interviewer would ask next. Try answering before peeking at the approach.
Red flags and common mistakes that signal junior thinking. Click to expand.
Treating per-step errors as additive instead of multiplicative. A 90% step rate does not give 90% over ten steps; it compounds down to roughly 35%.
The night-before-the-interview bullets. Scan these on the way to the call.
Primary sources. Skim if you want the original framing.