A steel rod is tested for two attributes torque strength and density. The probab

Question

A steel rod is tested for two attributes torque strength and density. The probability that a steel rod passes the torque test is 0.92. The probability that a steel rod meets the density specification is 0.90. Given that a steel rod passes the torque test, the probability it meets density specifications is .95. a. What is the probability that a random steel rod will fail at least one of the two test? b. Given that a steel rod meets density specifications, what is the probability that it passes the torque test?

Explanation / Answer

P(Torque Test) = P(A) = 0.92

P(density specification) = P(B) = 0.90

P(B/A) = 0.95

a. Pr( will fail one of the two tests) = P( pass torque test) * P( fail density test) + P( faile torque test) * P( fail density test) = 0.92 * ( 1- 0.90) + 0.90 * ( 1- 0.92) = 0.164

so it is 16.4 % probability that it will one of the two tests.

b. Pr ( Meets density specificantion it will pass density test too) = P(A/B) = P(B/A) * P(A) / P(B)

P(A/B) = P(B/A) * P(A) / P(B) = 0.95 * 0.92/ 0.90 = 0.971

c. Events C = a steel rod passes the torque test =P(A) = 0.92

Event D = a steel rod passed the density specifications = P(B) = 0.90

if the events are independent

then P(A   B) = P(A) .P(B)

so Here in this case P(A   B) = P(A/B) * P(B) if both events are independent

so P(A   B) = 0.971 * 0.90 = 0.8739 which is not equal to P(A) * P(B) =0.92 * 0.90 = 0.828

so both events are not indpendent.

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