In order to vertically integrate, Lang Lawnmower Limited has decided to buy a fi
ID: 3351889 • Letter: I
Question
In order to vertically integrate, Lang Lawnmower Limited has decided to buy a firm which manufactures lawnmower fasteners. Upon contacting the U.S. Dept. of Commerce, Lang finds that all fastener manufacturers are located in only three states. 50% of all fastener manufacturers are located in Michigan, 30% in Illinois, and the remainder in New York. Upon contacting the Departments of Commerce in these three states, Lang finds that fastener manufacturers have one of three forms of legal organization – a proprietorship, a partnership, or a corporation. In Michigan, 34% of fastener manufacturers are organized as proprietorships, 28% as partnerships, and the remainder as corporations. In Illinois 50% are proprietorships, 40% are partnerships, and the remainder are corporations. Finally, in New York, there are no proprietorships, 35% partnerships, and the remainder corporations.
Based on this information, Lang completed the following table of joint probabilities:
Location
Michigan
Illinois
New York
Form of Organization
Proprietorship
0.17
0.15
0.00
Partnership
0.14
0.12
0.07
Corporation
0.19
0.03
0.13
Answer the following questions:
If Lang randomly selects one fastener manufacturer, what is the probability that:
a) The manufacturer is from Illinois?
b) The manufacturer is in the form of a partnership, and is from New York?
c) The manufacturer is either from Illinois, or has the form of a corporation, or both?
d) The manufacturer is either from Illinois or has the form of a corporation, but not both?
e) The firm is from Michigan, given its form is a proprietorship?
f) The firm is not a corporation, and is from the Midwest (Michigan or Illinois)?
Location
Michigan
Illinois
New York
Form of Organization
Proprietorship
0.17
0.15
0.00
Partnership
0.14
0.12
0.07
Corporation
0.19
0.03
0.13
Explanation / Answer
Michigan Illinois New York Total
Proprietorship 0.17 0.15 0.00 0.32
Partnership 0.14 0.12 0.07 0.33
Corporation 0.19 0.03 0.13 0.35
-------------------------------------------------------------------------------------------------------------------------
Total 0.50 0.30 0.20 1.00
(a) P(Illinois) = 0.30
(b) P(Parnership & New York) = 0.00
(c) P(Illinois OR Corporation OR both) = 0.30 + 0.35 = 0.65
(d) P(Illinois OR Corpoation NOT both) = 0.30 + 0.35 - 0.03 = 0.62
(e) P(Michigon/Proprietorship) = P(Michigon & Proprietorship)/P(Proprietorship) = 0.17/0.32 = 0.5313
(f) P(Michigon OR Illinois) = P(Michigon) + P(Illinois) = 0.50 + 0.30 = 0.80
P(NOT Corporation) = 1 - 0.35 = 0.65
P(NOT Corporation & Midwest) = P(NOT Corporation) X P(Midwest) = 0.80 X 0.65 = 0.52
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