Question: 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 women engineering 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.

a. What is the probability of selecting a student who plans foreign language classes and graduate study?

b. What is the probability of selecting a women engineer who does not plan graduate study?

c. 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?