Probability question

part b:
see attached diagram

part e: 
$$P(G|FP)$$by the definition of conditional probability:
$$= \frac{P(GFP)}{P(FP)}$$by the Law of Total Probability:
$$= \frac{P(GFP)}{P(FP|G)P(G)+P(FP|G')P(G')}$$
$$= \frac{(.001)(.995)(.9999)}{(.995)(.9999)(.001)+(.03)(.002)(.999)}$$
$$\approx .9432$$