In the following study, three different universities have been tracking a select group of professors over the course of their employment at that university to determine the number of students who are in a particular professor’s classes, how many of those students have graduated, and if any of them have had their work published. In the attached Excel file, Probabilities, are the totals for each of the professors at the three different universities that participated in the study. Note: Be sure to use five (5) decimal places for your probabilities in the table, as some of them will be quite small. Do not convert to percentages as we are interested in probabilities only here.

1. The overall probability of students graduating at each of the three universities - P(Graduated)
2. The overall probability of students having a publication at each of the three universities - Rank by P(G)
3. The overall probability of students having a publication, given that they graduated at each of the three universities - P(Publications)
4. The probability of a student graduating for each professor - Rank by P(P)
5. The probability of a student having a publication for each professor - P(P|G)
6. The probability of a student having a publication given that they graduated for each professor - Rank by P(P|G)
7. Rank the professors within each university for each of the probabilities in 4–6. Then find the sum of the ranks and determine an overall ranking for each professor. Sum of Ranks and Overall Ranks

University/College	Professor	#of students taught	Graduated	Publication	P(Graduated)	Rank by P(G)
WWCC	J.W. Blake	2541	2134	704
	K.R. Cunningham	2378	1831	842
	R.H. Doughty	1942	1864	615
	L.M. Edwards	1044	1002	411
	W.H. Greiner	2219	2152	882
	I.D. Jackson	2243	2198	659
	O.P. Lawson	874	874	219
	G.F. Nelson	1202	1118	559
	A.F. Paul	1199	995	279
	D.K. Raulson	597	496	233
	T.R. South	1702	1345	551
	E.A. Thomas	2422	2180	567
	C.F. Viney	1724	1293	388
	F.E. Yousef	980	804	209
	TOTALS

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Given that Let p denote the Publications G denotes the Graduate ... View the full answer