The number of doctorates conferred in the social sciences and the physical scien
ID: 3038485 • Letter: T
Question
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)Explanation / Answer
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(Hc) = 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(Hc Kc) = P(H U K)c = 1 - P(H U K) = 1 - 0.6 = 0.4