Women are not explicitly prohibited from playing in the NBA but no female player has quite made it to the level of the men playing in the NBA in terms of skill and physical ability. With the continuing increase in participation in amateur (primarily NCAA) Basketball as well as professional ball (such as the WNBA) and consequent increased skill from improving level of competition in women's basketball it is conceivable that a woman may play in the NBA in the not to distant future.
-However-
Even if some women make it onto NBA teams it is unlikely they will ever make up a very large part of the teams because statistics are against them:
The same factors are also reflected in the lack of women in other major sports. While there are girls and women who have played on some high school and even college teams with boys and men in football, basketball, and Baseball (not sure about hockey), none have quite been good enough yet to make it into the top professional leagues.
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They can. Women actually have their own professional league. I don't think it's as national as the MLB, but it's pretty competitive stuff. I enjoy going downtown and watching the Akron Racers play. They don't do anything different than the guys except it's fast-pitch softball. It can get pretty hardcore.
Actually they can. But in the American tradition it isn't formal for women to do.