 There are two points to notice. The first is that in practice there is typically a trade-off between precision and recall, and the costs to you of each will vary from one problem to another. A trade-off of precision and recall that suits detecting credit card fraud may not suit detecting cancer, even if the frequencies of positive instances are identical. The point of training a classifier on known data is to make predictions on out of sample instances. So, tuning your classifier to yield a suitable trade-off between precision and recall in your training data is no guarantee that you will see this trade-off generalize.