Consider your Statistics 213 lecture section. There are 120 students registered.

Question

Consider your Statistics 213 lecture section. There are 120 students registered. Of these 120 students, 52 are Haskayne School of Business students (the remaining students belong to some other faculty). Moreover, 70 students are classified as 1st-Year students and 20 are 1st-Year students and who are not Haskayne 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 Haskayne-student, and 1st1st 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.

  

  

Part (b) Find the probability that the student you randomly chose is a Haskayne 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 Haskayne student nor in their 1st-Year.

(use four decimals)

Part (d) What proportion of all the students in your Statistics 213 lecture section are 1st-year students who are not in the Haskayne School of Business?

(use four decimals)
Part (e) Are the events HS and 1st mutually exclusive events? Select the most appropriate reason below.
A. HS and 1st1st are mutually exclusive events, because P(HS1st)=0P(HS1st)=0.
B. HS and 1st1st are not mutually exclusive events, because P(HS1st)P(HS)P(1st)P(HS1st)P(HS)P(1st).
C. HS and 1st1st are not mutually exclusive events, because P(HS1st)0P(HS1st)0.
D. HS and 1st1st are mutually exclusive events, because P(HS1st)=0P(HS1st)=0.
E. HS and 1st1st are mutually exclusive events, because P(HS1st)=P(HS)P(1st)P(HS1st)=P(HS)P(1st).

Part (f) Are the events HSHS and 1st1st independent events? Select the most appropriate reason below.
A.HS and 1st1st are independent events, because P(HS1st)=P(HS)P(1st)P(HS1st)=P(HS)P(1st).
B.HS and 1st1st are not independent events because P(HS1st)=0P(HS1st)=0.
C.HS and 1st1st are not independent events because P(HS1st)0P(HS1st)0.
D.HS and 1st1st are independent events because P(HS1st)0P(HS1st)0.
E.HS and 1st1st are not independent events, because P(HS1st)P(HS)P(1st)P(HS1st)P(HS)P(1st).
F. HS and 1st1st are independent events because P(HS1st)=0P(HS1st)=0.

HS HSc Row Probabilities 1st 1stc Column Probabilities

  

  

Explanation / Answer

from above:

dividing each cell by 120;

a)

b) probability that the student you randomly chose is a Haskayne student or in their 1st-Year

=0.4167+0.0167+0.1667 =0.60

c)probability that the student you randomly chose is neither a Haskayne student nor in their 1st-Year. =0.4

d) What proportion of all the students in your Statistics 213 lecture section are 1st-year students who are not in the Haskayne School of Business =0.1667

e)C. HS and 1st1st are not mutually exclusive events, because P(HS1st)0

f)E.HS and 1st1st are not independent events, because P(HS1st)P(HS)P(1st)

HS HSc Row total 1st 50 20 70 1stc 2 48 50 Column total 52 68 120

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