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Equation 3 · Part 1 · From Origins to Frontier: A History of Robotics and Embodied AI

Symbol P_finish

Pfinish≈(1−q)L.P_{\mathrm{finish}} \approx (1-q)^{L}.
PfinishP_{\mathrm{finish}}

What this part means

PfP_finish is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

PfP_finish is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

The arithmetic behind that result is worth making explicit, because it explains why the next eighteen months mattered more than the raw distance suggests. If a course of length L miles must be driven without a mission-ending error, and a vehicle’s probability of such an error is q per mile and roughly independent from one mile to the next, the probability of finishing the course is approximately Pfinish≈(1−q)LP_{\mathrm{finish}} \approx (1-q)^{L}. Over a 142-mile course, even a per-mile reliability of 99 percent yields a finishing probability under 25 percent, and the 2004 fleet did not come close to that bar. This is illustrative arithmetic rather than a number drawn from any cited study, but it frames what changed by…

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Sources cited in the surrounding passage

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