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One hundred students are questioned about their course of study and plans for graduate study. Let A = the event the student is male; B = the event the student is studying engineering; C = the event the student plans at least one year of foreign language; D = the event the student is planning graduate study (including professional school). The results of the survey are:

There are 55 men students; 23 engineering students, 10 of whom are women; 75 students will take foreign language classes, including all of the women; 26 men and 19 women plan graduate study; 13 male engineering students and 8 womenengineering students plan graduate study; 20 engineering students will take a foreign language and plan graduate study; 5 non engineering students plan graduate study but no foreign language courses;11 non engineering, women students plan foreign language study and graduate study.

  1. What is the probability of selecting a student who plans foreign language classes and graduate study?
  2. What is the probability of selecting a women engineer who does not plan graduate study?
  3. What is the probability of selecting a male student who either studies a foreign language but does not intend graduate study or will not study a foreign language but plans graduate study?
% file npr02_14.m % Data for [link] % A = male; B = engineering; % C = foreign language; D = graduate studyminvec4 DV = [A|Ac; A; B; Ac&B; C; Ac&C; A&D; Ac&D; A&B&D; ... Ac&B&D; B&C&D; Bc&Cc&D; Ac&Bc&C&D];DP = [1 0.55 0.23 0.10 0.75 0.45 0.26 0.19 0.13 0.08 0.20 0.05 0.11];TV = [C&D; Ac&Dc; A&((C&Dc)|(Cc&D))];disp('Call for mincalc') npr02_14Variables are A, B, C, D, Ac, Bc, Cc, Dc They may be renamed, if desired.Call for mincalc mincalcData vectors are linearly independent Computable target probabilities1.0000 0.3900 2.0000 0.2600 % Third target probability not calculableThe number of minterms is 16 The number of available minterms is 4Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMA
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A survey of 100 students shows that: 60 are men students; 55 students live on campus, 25 of whom are women; 40 read the student newspaper regularly, 25 of whom are women; 70 consider themselves reasonably active in student affairs—50 of these live on campus; 35 of the reasonably active students read the newspaper regularly; All women who live on campus and 5 who live off campus consider themselves to be active; 10 of the on-campus women readers consider themselves active, as do 5 of the off campus women; 5 men are active, off-campus, non readers of the newspaper.

  1. How many active men are either not readers or off campus?
  2. How many inactive men are not regular readers?
% file npr02_15.m % Data for [link] % A = men; B = on campus; C = readers; D = active minvec4DV = [A|Ac; A; B; Ac&B; C; Ac&C; D; B&D; C&D; ... Ac&B&D; Ac&Bc&D; Ac&B&C&D; Ac&Bc&C&D; A&Bc&Cc&D];DP = [1 0.6 0.55 0.25 0.40 0.25 0.70 0.50 0.35 0.25 0.05 0.10 0.05 0.05];TV = [A&D&(Cc|Bc); A&Dc&Cc];disp('Call for mincalc') npr02_15Variables are A, B, C, D, Ac, Bc, Cc, Dc They may be renamed, if desired.Call for mincalc mincalcData vectors are linearly independent Computable target probabilities1.0000 0.3000 2.0000 0.2500The number of minterms is 16 The number of available minterms is 8Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMA
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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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