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

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 tests? b. Given that a steel rod meets density specification, what is the probability that it passes the torque test? Are the events "a steel rod passes the torque test" and a steel rod meets the density specification" independent or dependent? Explain with numbers.

Explanation / Answer

1)P(Failing in atleast one) = 1-P(passing in both) = 1-0.92*0.90 = 0.172

2) P(Meets Density) = P(meet density/meets torque)P(Meets torque) + P(meet density/does not meets torque) P(Does not meet torque)

0.90 = 0.95 * 0.92 + 0.08 * P(meet density/does not meets torque)

or P(meet density/does not meets torque) =( 0.90 - 0.874)/0.08 = 0.325

3) These are independent events because probability of passing one does not increase passing of other. It is merely a relationship.

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