Question

7. Employees of a local university have been classified according to gender and job type as shown below Sex Job Faculty (FA) Salaried staff (SS) Male (M) 110 30 60 Female (F) 10 50 Hourly staff (HS) (A) If an employee is selected at random what is the probability that the employee is male? (B) If an employee is selected at random what is the probability that the employee is male and salaried staff? (C) If an employee is selected at random what is the probability that the employee is female given that the employee is a salaried member of sta (D) If an employee is selected at random what is the probability that the employee is female or works as a member of the faculty? (E) If an employee is selected at random what is the probability that the employee is female or works as an hourly staff member? (F) If an employee is selected at random what is the probability that the employee is a member of the hourly staff given that the employee is female? (G) If an employee is selected at random what is the probability that the employee is a member of the faculty? (H) Are gender and type of job mutually exclusive? Explain with probabilities (I) Are gender and type of job statistically independent? Explain with probabilities

Answer 1

Job                              Male             Female              Total

Faculty                       110                     10               120

Salaried staff                30                       50              80

Hourly staff                   60                     40              100

Total                            200                      100           300

(A) P(Male) = 200/300 = 0.6667

(B) P(Male & Salaried) = 30/300 = 0.1

(C) P(Female/Salaried) = P(Female & Salaried)/P(Salaried) = 50/80 = 0.625

(D) P(Female OR Faculty) = P(Female) + P(Faculty) - P(Female & Faculty)

                                        = 100/300 + 120/300 - 10/300

                                         = 0.3333 + 0.4 - 0.0333

                                           = 0.7

(E) P(Female OR Hourly staff) = P(Female) + P(Hourly staff) - P(Female & Hourly staff)

                                             = 100/300 + 100/300 - 40/300

                                            = 0.3333 + 0.3333 - 0.0.1333

                                            = 0.53333

(F) P(Hourly staff/Female) = P(Hourly staff & Female)?P(Female) = 40/100 = 0.4

(G) P(Faculty) = 120/300 = 0.4

(H) Gender & Type of job:

P(Male) = 200/300 = 0.6667

P(Faculty) = 120/300 = 0.4

So,

P(Male) X P(Faculty) = 0.6667 X 0.4 = 0.2667

But, P(Male & Faculty) = 110/300 = 0.3667

So, Gender & Type of job are dependent.

FIRST 4 QUESTIONS ARE ANSWERED AS PER DIRETIONS FOR ANSWERING.