Question

Size of a firm matters for implementation of supply chain management practices. It implies that larger firms very frequently implement supply chain and use advanced technologies to integrate supply chain partners. A study has reported part of the relationship between types of firm (Private and Public) and supply chain management implementation and between size of a firm (small to large, in terms of number of employees) and supply chain management implementation in International Journal of Business Modelling and Supply Chain Management (Vol. 5, 2013). The following table shows number of different sized private and public firms participated in this study:

	Private	Public	Total
≤ 24 employees	20	1	21
25-49	17	1	18
50-99	14	1	15
100-199	9	0	9
≥ 200 employees	23	9	32
Total	83	12	95

Two following events are defined:

A: {A firm participated in this study is Private}

B: {A firm participated in this study has employees more than 49}

Find

a. P(A) and P(B)​

b. P(AUB) ​​​​​​​​​

c. P(AnB) ​​​​​​​​​

Answer 1

Solution

Back-up Theory

Probability of an event E, denoted by P(E) = n/N ………………………………..............………………(1)

where

n = n(E) = Number of outcomes/cases/possibilities favourable to the event E and

N = n(S) = Total number all possible outcomes/cases/possibilities.

For 2 events, A and B,

P(A or B) = P(A ∪ B) = P(A) + P(B) - P(A ∩ B), ........................…………….................………………(2)

Now to work out the solution,

Part (a)

P(A) = probability that a firm participated in this study is Private

= Total number of Private firms/Total number of firms [vide (1)]

= 83/95

= 0.8737 Answer 1

P(A) = probability that a firm participated in this study has employees more than 49

= Total number of firms with more than 49 employees/Total number of firms [vide (1)]

= (15 + 9 + 32)/95 [vide (1)]

= 0.5895 Answer 2

Part (b)

P(AUB)

= P(A) + P(B) - P(A ∩ B)   [vide (2)]

Now,

P(A ∩ B) = probability that a firm participated in this study is Private and employees

more than 49 employees

= (14 + 9 + 23)/95 [vide (1)]

= 0.4842………………………………………………………………………….......................………….. (3)

Thus,

P(A ∩ B) = 0.8737 + 0.5895 – 0.4842 [vide Answers 1, 2 and (3)]

= 0.9790 Answer 3

Part (c)

P(A and B)

= P(A ∩ B)

= 0.4842 [vide (3)]    Answer 4

DONE