A woman is expecting her second child. Her doctor has told her that she has a 50-50 chance of having another girl. If she has another girl, there is a 70% chance that she will be taller than the first child. If she has a boy, however, there is only a 25% chance that he will be taller than the first child. If the second child is taller than the first, what is the probability that second child is a girl? Round your answers to three decimal places.