Question

PROBLEM 2 (30pts) The following two questions appear on an employee questionnaire:

(Q1) Is the corporation willing to listen to and fairly evaluate new ideas?

(Q2) How often are my coworkers important in my overall job performance?

Each answer allows one of five possible answer: 1 (never) ; 2 (seldom) ; 3 (usually) ; 4 (often) ; 5 (always)

(a)(4pts) Give the sample space, S, for answers to the ordered pair (Q1 , Q2). Then give the number of elements in S.

Answer:

(b)(4pts) Identify the subset of S that corresponds to the event, A, that, in words, is: “The corporation usually listens to and fairly evaluates new ideas.”. Then give the number of elements in A.

Answer:

(c)(4pts) Identify the sample space for only Q1, S_Q1, and then identify the subset, B, of this sample space that corresponds to the event given in words in (b). Give the number of elements in B.

Answer:

(d)(4pts) Consider the event, C, that, in words, is: “The corporation seldom, if ever, listens to and fairly evaluates new ideas and my coworkers are often (or always) important in my overall job performance.” Give the subset of S that corresponds to this event. Also, give the number of elements in this subset.

Answer:

(e)(4pts) Consider the event, D, that, in words, is: “Given that the corporation seldom, if ever, listens to and fairly evaluates new ideas, my coworkers are often (or always) important in my overall job performance.” Give the subset of S that corresponds to this event. Also, give the number of elements in this subset.

Answer:

(f)(5pts) In (e) the ‘given’ condition, call it G, is said to restrict the original sample space, S. Give this restricted sample space as a set. Then give the number of elements in it.

Answer:

(g)(5pts) You should have found that the sample space for (Q1,Q2) has 25 elements in it. For simplicity, assume that each element has probability 1/25. Compute the probabilities of the events in (d) and (e-f).

Solution:

(d):

(e-f):

Answer 1