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Bayes' Theorem — Update Probabilities with Evidence

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StatisticsCommon Core VAR-4.EPROBVerified correct ✓

Worked examples

The probability that a randomly selected item is defective is 1/20. The probability that the a quality inspection flags a defective item correctly is 80/100. The probability that it incorrectly flags a non-defective item is 1/100. Given that the a quality inspection gives a positive result, what is the probability that the item truly is defective? (Use Bayes' theorem.)
Answer: 0.8081
The probability that a randomly selected item has the disease is 1/50. The probability that the a diagnostic test tests positive given the disease is present is 99/100. The probability that it tests positive when the disease is absent (false positive) is 10/100. Given that the a diagnostic test gives a positive result, what is the probability that the item truly has the disease? (Use Bayes' theorem.)
Answer: 0.1681

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