The number of doctorates conferred in the social sciences an

The number of doctorates conferred in the social sciences and the physical sciences during 1998 is shown in the following table. The data are classified as being a U.S. citizen or a foreign-born citizen. For the events labeled in the table as A, B, C, and D, answer the following: Determine P(A). Determine P(D). Determine the probability that the doctorate is in social sciences and is conferred on a U.S. citizen. Determine the probability that the doctorate is in physical sciences or is conferred on a foreign-born citizen Let K and H be two events of an experiment with sample space S. Suppose P(K) =.3, P(H Intersection K) = .1 and P(H^c) = .6 Find each of the following: P(H) P (H Union K) P(H^c Intersection K^c)

Solution

2) a) P(A) = 3113 / 6639 = 0.47

b) P(D) = 1871 / 6639 = 0.28

c) P(A and C) = 760 / 6639 = 0.11

d) P(B or D) = P(B) + P(D) - P(B and D)

                    = 3526/6639 + 1871/6639 - 1111/6639

                    = 0.65

3) a) P(H) = 1 - P(H^c) = 1 - 0.6 = 0.4

b) P(H U K) = P(H) + P(K) - P(H K)

                   = 0.4 + 0.3 - 0.1

                   = 0.6

c) P(H^c K^c) = P(H U K)^c = 1 - P(H U K) = 1 - 0.6 = 0.4