In the survey of MBA students, the following data were obtained on "students" first reason for application to school in which they matriculated."
Reason for application 


School quality 
school cost 
Other 
Total 
Enrollment 
Full time 
421 
393 
76 
890 
status 
part time 
400 
593 
46 
1039 

Total 
821 
986 
122 
1929 
a. Make a joint probability table for such data.
b. Employ the marginal probabilities of school quality, school cost or convenience, and other to comment on most important reason for selecting a school.
c. If a student goes full time, find out the probability that school quality is the first reason for selecting a school?
d. If a student goes part time, find out the probability that school quality is the first reason for selecting a school?
e. Let A denote the event that the student is full time and B denote the event that the student lists school quality as the first reason for applying. Are events A and B independent? Justify your answer.