A census of Americans over 60 years of age who have a post-graduate degree examined the relationship between age and type of post-graduate degree produced the following table of probabilities.

Age	P(Master’s Degree)	P(Professional Degree)	P(Doctorate Degree)
60–64	.72	.18	.10
65–74	.68	.17	.15
75+	.60	.20	.20

The proportion of Americans 60 years of age and older in each of the age categories is listed next. 

P(60–64) = 33%, P(65–74) = 44%, P(75 and older) = 23%

a. What is the probability that a randomly selected American who is older than 60 and possesses a post-graduate degree has a doctorate?

b. Find the probability that an American who is 60 years old with a post-graduate degree has a Master’s degree.