Question

# There are 120 students registered in a class. Of these 120 students, 52 are Business students...

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 1st-Year students and 20 are 1st-Year 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 Business-student, and

1st represent the event that this chosen student is a 1st-Year 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 1st-Year. 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 1st-Year.

(use four decimals)

Part (d) What proportion of all the students in the class are 1st-year 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 1st-Year

=72/120 =0.6

c)

probability that the student you randomly chose is neither a Business student nor in their 1st-Year =1-0.6 =0.4

d)

proportion of all the students in the class are 1st-year 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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