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Say I bought two tests for lead in water: X and Y . Test X indicates...

Say I bought two tests for lead in water: X and Y . Test X indicates there’s lead in the water 95% of the time when it is present but has a 10% false positive rate (the times when it detects lead, but it’s not actually there). Test Y is 90% effective at recognizing lead but has a 5% false positive rate. The tests use independent methods of identifying lead which occurs in 3% of houses.

(a) Write the statements above as a set of (conditional) probabilities. Define the terms used in your notation.

(b) Now, say that a I test my water for lead using only one test, and the test comes back positive (indicating lead is present). What are the conditional probability values I need to calculate to determine which test would be more indicative that I really had a lead problem?

(c) Given the above, can you determine which test would be more indicative that I really had a problem? Show your work.

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