Problem

A process gives \(\text{three}\) departments equal probability, then draws a uniform employee within the designated department; sizes are \(2\), \(5\), and \(8\). Compute individual probabilities and audit fairness, efficiency, and transparency.

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Call it inefficient despite acceptance 1 and expected selections 1; individual chances are unequal but the process is transparent.

It is efficient and transparent but unfair to individuals: member probabilities are 1/6, 1/15, and 1/24 by department.

Call it fair because departments are selected 1/3 each; individual probabilities remain 1/6,1/15,1/24, acceptance is 1, and the process is transparent.

Call the published process opaque; it accepts every selection efficiently but individual probabilities 1/6,1/15,1/24 are unfair.

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A process gives \(\text{three}\) departments equal probability, then draws a uniform employee within the designated department; sizes are \(2\), \(5\), and \(8\). Compute individual probabilities and audit fairness, efficiency, and transparency.

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