Question 3:
A. Probability of being in the private sector or indicating talent management as a priority:
P(Private or Talent Management) = P(Private) + P(Talent Management) - P(Private and Talent
Management)
= 347/536 + 222/536 - (156/536)
= 413/536
≈ 0.7705 or 77.05%
B. Probability of being in the public sector and not indicating cost management as a future priority:
Total HR professionals in the public sector = 189
HR professionals in public sector not indicating cost management as a priority = 72
Total HR professionals = 536
Probability = (HR professionals in public sector not indicating cost management) / Total HR
professionals
= 72 / 536
≈ 0.1343 or 13.43%
C. Probability of not indicating cost management as a future priority in his/her organization or being
in the public sector:
P((Not Cost Management) or Public) = P(Not Cost Management) + P(Public) - P((Not Cost
Management) and Public)
P(Not Cost Management) = Total Not Cost Management / Total HR Professionals= 291 / 536
P(Public) = Total in Public Sector / Total HR Professionals= 189 / 536
P((Not Cost Management) and Public) = (72 / 536)
P((Not Cost Management) or Public) = (291 / 536) + (189 / 536) - (72 / 536)
= 408 / 536
= 51 / 67
≈ 0.7612 or 76.12%
D. Probability of not indicating cost management as a future priority in his/her organization or being
in the public sector:
P((Not Cost Management) or Public) = P(Not Cost Management) + P(Public) - P((Not Cost
Management) and Public)
P(Not Cost Management) = Total Not Cost Management / Total HR Professionals
= 291 / 536
P(Public) = Total in Public Sector / Total HR Professionals
= 189 / 536
P((Not Cost Management) and Public) = (72 / 536)
P((Not Cost Management) or Public) = (291 / 536) + (189 / 536) - (72 / 536)
= 408 / 536
= 51 / 67
≈ 0.7612 or 76.12%
E.To determine if "cost management is a priority" and "sector" are independent, we need to check if
P(A∩ B) = P(A) * P(B), where A is the event "cost management is a priority" and B is the event "sector".
If this condition holds, the events are independent
P(A ∩ B) = (Total HR professionals indicating cost management) / Total HR professionals
= 245 / 536≈ 0.4571 or 45.71%
P(A) = Total HR professionals indicating cost management / Total HR professionals
= 245 / 536≈ 0.4571 or 45.71%
P(B) = Total HR professionals in the private sector / Total HR professionals
= 347 / 536≈ 0.6474 or 64.74%
≈ 0.4571 or 45.71%
P(B) = Total HR professionals in the private sector / Total HR professionals
= 347 / 536≈ 0.6474 or 64.74%
P(A) * P(B) ≈ 0.4571 * 0.6474 ≈ 0.2952
Since P(A ∩ B) ≠ P(A) * P(B), cost management being a priority and sector are not independent
F. To determine if "talent management is a priority" and "sector" are independent, we need to check
if P(C ∩ D) = P(C) * P(D), where C is the event "talent management is a priority" and D is the event
"sector". If this condition holds, the events are independent.
P(C ∩ D) = (Total HR professionals indicating talent management) / Total HR professionals
= 222 / 536≈ 0.4142 or 41.42%
P(C) = Total HR professionals indicating talent management / Total HR professionals
= 222 / 536≈ 0.4142 or 41.42%
P(D) = Total HR professionals in the private sector / Total HR professionals
= 347 / 536≈ 0.6474 or 64.74%
P(C) * P(D) ≈ 0.4142 * 0.6474 ≈ 0.2680
Since P(C ∩ D) ≠ P(C) * P(D), talent management being a priority and sector are not independent.