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In different lights the formula [''m'',''b''] = [''m'',][''b''] presents itself as an "aimed arrow", "fair sample", or "independence" condition.  I had taken the tack of illustrating this polymorphous theme in bas relief, that is, via detour through a universe of discourse where it fails.  Here's a brief reminder of the Othello example:

In different lights the formula <math>[\mathrm{m,}\mathrm{b}] = [\mathrm{m,}][\mathrm{b}]</math> presents itself as an ''aimed arrow'', ''fair sample'', or ''statistical independence'' condition.  The concept of independence was illustrated above by means of a contrasting case.  For ease of reference, the details of that counterexample are summarized below.

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The condition, "men are just as apt to be black as things in general", is expressible in terms of conditional probabilities as P(''b''|''m'') = P(''b''), written out, the probability of the event Black given the event Male is exactly equal to the unconditional probability of the event Black.

The condition that "men are just as apt to be black as things in general" can be expressed in terms of conditional probabilities as <math>\operatorname{P}(\mathrm{b}|\mathrm{m}) = \operatorname{P}(\mathrm{b}),</math> which means that the probability of the event <math>\mathrm{b}\!</math> given the event <math>\mathrm{m}\!</math> is equal to the unconditional probability of the event <math>\mathrm{b}.\!</math>

Thus, for example, it is sufficient to observe in the Othello setting that P(''b''|''m'') = 1/4 while P(''b'') = 1/7 in order to cognize the dependency, and thereby to tell that the ostensible arrow is anaclinically biased.

Thus, for example, it is sufficient to observe in the Othello setting that P(''b''|''m'') = 1/4 while P(''b'') = 1/7 in order to cognize the dependency, and thereby to tell that the ostensible arrow is anaclinically biased.