Practice problem
Conditional Probability: Two-Way Tables
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There are only a few classical example of conditional probability, although it is widely used to test effectiveness. With this in mind, consider the following.
A factory (Generic Inc. or GI) produces the highly-important ombejteaclt, vital to the world's economy. It is so vital and hard to produce that this factory wants to remove any defective ombejteaclts. Thus, GI has devised a test to test any ombejteaclt. The test is completely accurate for defective ombejteaclts (in that it always says the ombejteaclt is defective) but has a 1% chance of saying perfect ones are defective.
Every ombejteaclt has a 10% chance of being defective. I pick up a random ombejteaclt and test it. It turns up defective. What is the chance it is actually defective? Write as a fraction.
Finally, what if the test has a 10% error rate, and a 1% chance of being defective? What is the chance it is actually defective? Write as a fraction.