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And this, of course, is the definition of independent events, as applied to the event of being Black and the event of being a Man.

This, of course, is the definition of independent events, as applied to the event of being Black and the event of being a Man. It seems to be the most likely guess that this is the meaning of Peirce's statement about frequencies:

It seems like a likely guess, then, that this is the content of Peirce's statement about frequencies, [''m'',''b''] = [''m'',][''b''], in this case normalized to produce the equivalent statement about probabilities: P(''m'' & ''b'') = P(''m'')P(''b'').

| <math>[\mathrm{m,}\mathrm{b}] ~=~ [\mathrm{m,}][\mathrm{b}]</math>

 

in this case normalized to produce the equivalent statement about probabilities:

 

| <math>\operatorname{P}(\mathrm{m}\mathrm{b}) ~=~ \operatorname{P}(\mathrm{m})\operatorname{P}(\mathrm{b}).</math>

Let's see if this checks out.

Let's see if this checks out.