A random sample of the employees of the Hardware Manufa Comp

A random sample of the employees of the Hardware Manufa Company was chosen to determine their retirement plazas after age 65. T the sample were divided into management and production. What is the probability of choosing one employee who a. is a production employee?.8 b. is a production employee and an employee who plans to retire?.375 c. plans to retire or is in a management position?.37931034 d. plans to retire, given the employee is in a management position? .33?.. e. Are the events, retire and management, independent? Are the events, retire and management, mutually exclusive? g. Are the events, management and production, mutually exclusive? h. Are the events, retire and not retire, complements?

Solution

a) Prob for production employee = 80/100 = 0.8

b) Prob for production employee and plan to reitre= 30/100 =0.3

c) Prob (plans to retire or manger position) = (35+20-5)/100 =0.5

d) Prob (plans to retire given he is in management position) = 5/20 = 0.25

e) P(Retire) = 0.35 and P(Mgt) = 0.2

P(retire) P(Mgt) = 0.7 not equal to 0.05 P(retire and manage)

Hence the two are not independent.

f) No. Retire and management have intrsection hence not mut. exclusive

g) Yes. Mgt and production are mutually exclusive.

h) yes. Retire and non retire together give total no and their intersection is 0.

Hence they are complements