Question

(2) A university president has proposed that ,for graduation. Three bundred faculty members and studensts ro asked about their opinion on all students must take a course in ethics as a req uire- responses of these faculty members and students. this issue. The following table gives astica a two-way classification of the Favor Oppose Neutral Total Faculty 45 Student90 110 30 36 Total 0a135 1 40 300 Select one person at random from these 300 faculty members and students. (a) Find the probability that the chosen person 0) is a student or 1C0+3000) n opposes the issue: (ii) is in favor of the issue or is neutral: (ii) is a faculty member and is in favor of the issue: (iv) is a student, given that he/she is oppose this issue. (v) is oppose the issue, given that he/she is a students (c) Are the two events 'Oppose'and 'Student'independent? Why or why not?

Answer 1

A)

1)

P(student) = 230/300

P(opposes the issue) = 125/300

P(student and opposes the issue) = 110/300

P(student or opposes the issue) = P(student) + p(opposes the issue) - p(student and opposes the issue)

= 230/300 + 125/300 - 110/300

=245/300

=0.8166

2)

P(favors issue) = 135/300

P(neutral)= 40/300

P(favours issue and neutral) = 0/300

P(favors issue or neutral) = p(favours issue) + p(neutral) - p(favours issue and neutral)

= 135/300 + 40/300 -0

=175/300

=0.5833

3)

P(faculty member and favours issue) = 45/300

=0.15

4)

P(student and opposes the issue) = 110/300

P(oppose the issue) = 125/300

P(student | oppose the issue) = p(student and opposes the issue)/p(opposes the issue)

= (110/300) / (125/300)

= 110/125

=0.88

5)

P( opposite issue and student ) = 110/300

P(student) = 230/300

P(opposite issue | student) = p(opposite issue and student) / p(student)

= 110/230

=0.4783

B)

P(oppose issue) = 125/300

P(student) = 230/300

P(oppose issue and student) = 110/300 = 0.3666

For independent events ,

p( oppose issue and student) = p(oppose issue) * p(student)

Here , p(0ppose issue) * p(student)

= (125/300) * (230/300)

= 0.3194

p( oppose issue and student) ≠(oppose issue) * p(student)

So,they are not independent events