Edit: Actually, on thinking about it, I realize I'm being a doofus. You almost undoubtedly meant, not inferring A from G when A is more common in G than in the general population, but inferring A from G when A is more common than -A in G, which is a far more unreasonable thing to be upset about. My apologies.

Strictly speaking you should adjust your probability estimate of the person having attribute A either way. How you then act depends on the consequences of making either error., e.g., the consequences of falsely assuming someone isn't a violent criminal can be more serious then the reverse.