Changes

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That in itself is enough to puncture any notion that ''b'' and ''m'' are statistically independent, but let us continue to develop the plot a bit more.

That is enough to puncture any notion that <math>\mathrm{b}\!</math> and <math>\mathrm{m}\!</math> are statistically independent, but let us continue to develop the plot a bit more. Putting all of the general formulas and particular facts together, we arrive at following summation of situation in the ''Othello'' case:

 

Putting all of the general formulas and particular facts together, we arrive at following summation of situation in the Othello case:

If the fair sampling condition holds:

If the fair sampling condition holds:

: [''m'',] = [''m'',''b'']/[''b''] = [''b'']/[''b''] = `1`,

| <math>[\mathrm{m,}] ~=~ \frac{[\mathrm{m,}\mathrm{b}]}{[\mathrm{b}]} ~=~ \frac{[\mathrm{b}]}{[\mathrm{b}]} ~=~ \mathfrak{1}.</math>

In fact, however, it is the case that:

In fact, however, it is the case that: