user3237: I am NOT asking for the percentage of chess players that are women.
I am asking for the percentage of players who are women in the sections where both men and women can play in.
That percentage is obviously lower than the percentage of chess players that are women because many women prefer to play in women-only sections.
In other words the question could be rephrased as: if I'm a man and tomorrow I'll play a game in a tournament, what's the probability that my opponent is a woman?
You can answer for either USCF or FIDE, it doesn't matter which one.

user8923: In France, there are women only team championships but not all women chess players supports them.
Here is the point of view of Mathilde Choisy (WFM, FIDE 2181), in French http://echecsetmixte.fr/?p=665
The main points are : 

If you want to make progress, don't think about women competitions, think bigger and aim for results in "general" competitions. A top 20 in French mixed youngster championship is a better result than a top 3 in European Girl championship.
France has only a few active women players rated 2000+ so they always play against each other in these competitions
If you stay too long in girl competitions, you won't realize the gap in level with the boys until it's too late
Women championships promotes "amateur chess" but are no use for professionnal competitions.

It's clearly not an answer to the question but I think it's worth sharing.
Btw I met my wife in an French mixed open, so there are some chances that you'll played against some. I checked the data for this open and here are the rates :

Open A , Elo >1700 : 5-10% women
Open B, Elo <1800 : 12-15% women


3237: <p>I am NOT asking for the percentage of chess players that are women.</p>

<p>I am asking for the percentage of players who are women in the sections where both men and women can play in.<br>
That percentage is obviously lower than the percentage of chess players that are women because many women prefer to play in women-only sections.</p>

<p>In other words the question could be rephrased as: if I'm a man and tomorrow I'll play a game in a tournament, what's the probability that my opponent is a woman?</p>

<p>You can answer for either USCF or FIDE, it doesn't matter which one.</p>
 8923: <p>In France, there are women only team championships but not all women chess players supports them.</p>

<p>Here is the point of view of Mathilde Choisy (WFM, FIDE 2181), in French <a href="http://echecsetmixte.fr/?p=665" rel="nofollow">http://echecsetmixte.fr/?p=665</a></p>

<p>The main points are : </p>

<ul>
<li>If you want to make progress, don't think about women competitions, think bigger and aim for results in "general" competitions. A top 20 in French mixed youngster championship is a better result than a top 3 in European Girl championship.</li>
<li>France has only a few active women players rated 2000+ so they always play against each other in these competitions</li>
<li>If you stay too long in girl competitions, you won't realize the gap in level with the boys until it's too late</li>
<li>Women championships promotes "amateur chess" but are no use for professionnal competitions.</li>
</ul>

<p>It's clearly not an answer to the question but I think it's worth sharing.</p>

<p>Btw I met my wife in an French mixed open, so there are some chances that you'll played against some. I checked the data for this open and here are the rates :</p>

<ul>
<li>Open A , Elo >1700 : 5-10% women</li>
<li>Open B, Elo &lt;1800 : 12-15% women</li>
</ul>
