Question

A factory tests all its products. The proportion of defective items is 0.01. The probability that...

A factory tests all its products. The proportion of defective items is 0.01. The

probability that the test will catch a defective product is 0.95. The test will also

reject nondefective products with probability 0.01.

Given that a product passes the test, what is the probability that it is defective?

(b) Given that the product does not pass the test, what is the probability that the

product is defective?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Suppose we have 10000 items.

Number of defective items = 100

Number of non-defective items = 9900

Number of defective items that get rejected = 0.95*100 = 95

Number of defective items that get passed = 100-95 = 5

Number of non-defective items that get rejected = 0.01*9900 = 99

Number of non-defective items that get passed = 9900-99 = 9801

(a)

P(product is defective | it passes the test) = number of defective products that get passed/Number of products that get passed = 5/(5+9801) = 0.00051

(b)

P(product is defective | it gets rejected) = number of defective products that get rejected/Number of products that get rejected = 95/(95+99) = 0.486

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