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Equation 3 · Part 4 · From Origins to Frontier: A History of Robotics and Embodied AI

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Pfinish≈(1−q)L.P_{\mathrm{finish}} \approx (1-q)^{L}.
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

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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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.