Is there a name for this mis-application of marginal distributions? Recently I was shown some market research that was more or less equivalent to the following:


*

*50% of the population is female

*50% of the population is blonde

*therefore, our new hair dye for blonde women could appeal to 50% of the population.


I was about to mumble something about marginal distributions, but is there a name for this kind of reasoning? Ideally, something that non-statisticians could relate to?
 A: Denote (in proportions), $F$ for female and $nF$ for "non-female", $B$ for "blonde" and $nB$ for "non-blonde". The information 


*

*50% of the population is female

*50% of the population is blonde


permits us only to write
\begin{array}{| r | r | r | r|}
  \hline                       
     & \text {B} & \text{nB} &\Sigma \\
  \hline 
  \hline                       
  F &   &   & 0.5 \\
  \hline                     
nF &   &   & 0.5 \\
\hline
\Sigma & 0.5 & 0.5 & 1 \\
  \hline  
\end{array}
The "conclusion" from this information   


*

*therefore, our new hair dye for blonde women could appeal to 50% of the population.


appears to only imply that the following may hold:  
\begin{array}{| r | r | r | r|}
  \hline                       
     & \text {B} & \text{nB} &\Sigma \\
  \hline 
  \hline                       
  F & 0.5  &   & 0.5 \\
  \hline                     
nF &   &   & 0.5 \\
\hline
\Sigma & 0.5 & 0.5 & 1 \\
  \hline  
\end{array}
But hey, this leads to a unique full filling of the table: the "conclusion" necessarily implies that  
\begin{array}{| r | r | r | r|}
  \hline                       
     & \text {B} & \text{nB} &\Sigma \\
  \hline 
  \hline                       
  F & 0.5  & 0.0  & 0.5 \\
  \hline                     
nF &  0.0 & 0.5  & 0.5 \\
\hline
\Sigma & 0.5 & 0.5 & 1 \\
  \hline  
\end{array}
In other words: in order for it to be possible that our new hair dye for blonde women can appeal to $50\%$ of the population (given the information we have on it), it must be the case that  


*

*All females are blonde
and also that

*All non-females are non-blonde
I believe simple arithmetic is something that non-statisticians can relate to.
