Probability a component is declared defective given inspection accuracy

[sumans]

On the basis of past data, suppose it is known that 0.5% of a components of a particular type manufactured by a firm are defective. The quality inspection procedure is such that 90% of the defective components will actually be found defective and 3% of the non-defective components will also be wrongly declared defective. A component is selected at random from the manufacturing process and inspected.

a) What is the probability that the components is declared defective?

b) If the component is declared defective, what is the conditional probability that the item is actually defective?

 

[chroot]

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