If none of the causes are present, the corresponding probability is 0.05 ty of d

Question

If none of the causes are present, the corresponding probability is 0.05 ty of defective concrete on the project. [20 points] 3. Suppose that before a section of a newly constructed highway pavement is accepted by the State Department of Highway, the thickness of a 25 cm pavement is inspected for specification compliance by taking ultrasonic readings. Each section will be accepted if the measured thickness is atleast 23 cm; otherwise, the entire section will be rejected or a penalty will be imposed. Use the following notation: G constructed thickness of pavement is atleast 23 cm. A = ultrasonic measured thickness is atleast 23 cm. From past experience, 90% of constructed highway works by the same contractor were found to be in compliance with specifications, i.e. based on the contractor's past construction record. we may assume that 90% of his constructed pavement will have acceptable ultrasonic reading. P(A) = 0.9.

Explanation / Answer

P(A) = 0.9

P(Ac) = 1 - 0.9 = 0.1

P(G| Ac) = 1 - P(Gc|Ac) = 1 - 0.80 = 0.20

By theorem of total probability,

P(G) = P(G|A)*P(A) + P(G|Ac)*P(Ac) = 0.80*0.90 + 0.20*0.10 = 0.74

P(A | G) = P(G|A)*P(A) / P(G) = 0.80*0.90 / 0.74 = 0.9730

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