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
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

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 number of wells in each of the following events.

(a) A and B

(b) A'

(c) A or B

(d) A or B'

(e) A' and B'

Answer 1

from above:

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

b)

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

c)

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

d)

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