To ‘Tell’ the Truth Moderately Difficult

You’re playing poker against Tex. He has a ‘tell’: his eye twitches 90 per cent of the time when he thinks he has a good hand. The trouble is that he has a twitchy eye anyway, and there’s a 10 per cent chance it’s twitching even when he thinks his hand isn’t strong. If Tex considers 30 per cent of all the hands he gets to be good, and if his eye is twitching right now, what’s the probability that he thinks he has a good hand?