Changes

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"

| <math>\mathrm{m,}\mathrm{b} ~=~ \text{man that is black}</math>

| <math>\mathrm{m,}\mathrm{b} ~=~ \text{man that is black}.</math>

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represented below in the equivalent form:

This is represented below in the equivalent form:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"

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:

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:

If the fair sampling condition holds:

If the fair sampling condition were true, it would have the following consequence:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"

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In fact, however, it is the case that:

On the contrary, we have the following fact:

: [''m'',] = [''m'',1]/[1] = [''m'']/[1] = 4/7.

| <math>[\mathrm{m,}] ~=~ \frac{[\mathrm{m,}\mathbf{1}]}{[\mathbf{1}]} ~=~ \frac{[\mathrm{m}]}{[\mathbf{1}]} ~=~ \frac{4}{7}.</math>

In sum, it is not the case in the Othello example that "men are just as apt to be black as things in general".

In sum, it is not the case in the Othello example that "men are just as apt to be black as things in general".