There are 120 students registered in a class. Of these 120 students, 52 are Business students (the remaining students belong to some other faculty). Moreover, 71 students are classified as 1stYear students and 20 are 1stYear students and who are not Business students.
You are to randomly choose one student from the 120 in your lecture section. Let HS represent the event that the chosen student is a Businessstudent, and
1st represent the event that this chosen student is a 1stYear student.
Part (a) Complete the table below. Use four decimals in each of your answers.
HS 
HSc 
Row Probabilities 

1st 

1stc 

Column Probabilities 
Part (b) Find the probability that the student you randomly chose is a Business student or in their 1stYear. Enter your answer to four decimals.
Part (c) Find the probability that the student you randomly chose is neither a Business student nor in their 1stYear.
(use four decimals)
Part (d) What proportion of all the students in the class are 1styear students who are not in Business?
(use four decimals)
Part (e) Are the events HS and 1st mutually exclusive events? Select the most appropriate reason below.
A. HS and 1st are mutually exclusive events, because P(HS∩1st)=P(HS)P(1st)
B.HS and 1st are mutually exclusive events, because P(HS∩1st)=0
C. HS and 1st are not mutually exclusive events, because P(HS∩1st)≠0
D. HS and 1st are mutually exclusive events, because P(HS∪1st)=0
E. HS and 1st are not mutually exclusive events, because P(HS∩1st)≠P(HS)P(1st)
Part (f) Are the events HS and 1st independent events? Select the most appropriate reason below.
A. HS and 1st are not independent events because P(HS∩1st)=0
B. HS and 1st are independent events because P(HS∩1st)≠0
C. HS and 1st are not independent events, because P(HS∩1st)≠P(HS)∗P(1st)
D. HS and 1st are independent events because P(HS∩1st)=0
E. HS and 1st are not independent events because P(HS∩1st)≠0
F. HS and 1st are independent events, because P(HS∩1st)=P(HS)P(1st)
HS  Hsc  total  
1st  51  20  71 
1stc  1  48  49 
total  52  68  120 
dividing each value in above table by 120:
a)
HS  Hsc  total  
1st  0.4250  0.1667  0.5917 
1stc  0.0083  0.4000  0.4083 
total  0.4333  0.5667  1.0000 
b)
probability that the student you randomly chose is a Business student or in their 1stYear
=72/120 =0.6
c)
probability that the student you randomly chose is neither a Business student nor in their 1stYear =10.6 =0.4
d)
proportion of all the students in the class are 1styear students who are not in Business
=20/120 =0.1667
e)
C. HS and 1st are not mutually exclusive events, because P(HS∩1st)≠0
f) C. HS and 1st are not independent events, because P(HS∩1st)≠P(HS)∗P(1st)
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