Question

In: Statistics and Probability

As items come to the end of a production line, an inspector chooses which items are...

As items come to the end of a production line, an inspector chooses which items are to go through a complete inspection. Nine percent of all items produced are defective. Seventy percent of all defective items go through a complete inspection, and 30% of all good items go through a complete inspection. Given that an item is completely inspected, what is the probability that it is defective? Round your answer to four decimal places if necessary. (Do not round intermediate values.)

P(Defective|Inspected) = _________

a. 0.1745
b. 0.1864
c. 0.2743
d. 0.1875

Solutions

Expert Solution

Given that 9% of all items produced are defective. That is, P(Defective) = 0.09

P(Not Defective) = 1 - 0.09 = 0.91

Seventy percent of all defective items go through a complete inspection, that is,

P(Inspected | Defective ) = 0.70

and 30% of all good items go through a complete inspection, that is, P(Inpected | Not Defective) = 0.30

we want to find, P(Defective | Inspected)

P(Defective | Inspected ) = 0.1875

Answer: d) 0.1875

orchestra answered 2 years ago
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