Question

An article in The Journal of Data Science ["A Statistical Analysis of Well Failures in Baltimore County" (2009, Vol. 7, pp. 111-127)] provided the following table of well failures for different geological formation groups in Baltimore County. Wells Geological Formation Group Failed Total 170 1685 Gneiss Granite Loch raven schist 2 28 443 3733 Mafic 14 363 29 309 60 1403 Marble Prettyboy schist Other schists Serpentine 46 933 39 3 Let A denote the event that the geological formation has more than 1000 wells, and let B denote the event that a well failed. Determine the following probabilities. Round your answers to three decimal places (e.g. 98.765). (a) P(AB) = (b) P(A') = (c) P(AUB) = (d) P(AUB) (e) P(A' B') = ! 1 !

Answer 1

Geological Formation Group	Failed	Total
Gnesis	170	1685
Granite	2	28
Loch raven schist	443	3733
Mafic	14	363
Marble	29	309
Prettyboy schist	60	1403
Other schists	46	933
Serpentine	3	39
total	767	8493

a)

A and B =(170+443+60)=673

probability = 673/8493 = 0.079

b)

A' =28+363+309+933+39=1672

probability=0.197

c)

A or B =1685+2+3733+14+29+1403+46+3=6915

probability = 0.814

d)

P(A u B') = 1685+(28-2)+3733+(363-14)+(309-29)+1403+(933-46)+(39-3)= 8399/8493 = 0.989

e)

A' and B' =8493-(A or B) =8493-6915=1578

probability = 0.186

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