Question

PLEASE SHOW STEP BY STEP SOLUTION AND GIVE CORRECT ANSWER (VERY IMPORTANT).

Geological Formation Group Failed Total Gneiss 170 1885 Granite 2 28 Loch raven schist 523 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 of a well has more than 1000 wells, and let B denote the event that a well failed. Determine the following probabilities. Round your answers to four decimal places (e.g. 98.7654) (а) Р (An B) 3D (b) Р (A U B) 3D| (c) P (A' U B') = (d) Use the total probability rule to determine P (A).

Answer 1

failed	total
170	1885
2	28
523	3733
14	363
29	309
60	1403
46	933
3	39
847	8693

a)

P(A and B) = (170 + 523 + 60 ) / 8693

= 753/8693 = 0.0866

b)

P(A or B) = P(A) + P(B) - P(A and B)

P(A) = (1885 + 3733 + 1403 )/ 8693 = 0.8077

P(B) = 847/8693 = 0.0974

hence

P(A or B) = 0.8077 + 0.0974 - 0.0866

= 0.8185

c)

= 1 - P(A and B)

= 1- 0.0866

= 0.9134

d)

P(A) = 0.8077

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