On any given day, the probability that a large local river is polluted by a carb

Question

On any given day, the probability that a large local river is polluted by a carbon tetrachloride spill is 0.12. Each day, a test is conducted to determine whether the river is polluted by carbon tetrachloride. This test has proved correct 84 percent of the time. Use this information and a theoretical group of 10,000 days to construct a table for this testing scenario. Round all answers to two decimal places.

1. What proportion of days does the test indicate carbon tetrachloride pollution?

2. Suppose that on a particular day the test indicated carbon tetrachloride pollution. What is the probability that such pollution actually exists?

3. What proportion of days where the test is negative will the river actually be polluted?

(1 point) On any given day, the probability that a large local river is polluted by a carbon tetrachloride spill is 0.12. Each day, a test is conducted to determine whether the river is polluted by carbon tetrachloride. This test has proved correct 84 percent of the time. Use this information and a theoretical group of 10,000 days to construct a table for this testing scenario. Round all answers to two decimal places Pollution presentTest Positive Test Negative Total Yes No Total 10,000 1. What proportion of days does the test indicate carbon tetrachloride pollution? 2. Suppose that on a particular day the test indicated carbon tetrachloride pollution. What is the probability that such pollution actually exists? 3. What proportion of days where the test is negative will the river actually be polluted?

Explanation / Answer

from abvoe below is joint probability table:

1) proportion of days does the test indicate carbon tetrachloride pollution

=2416/10000 =0.2416

2)

P(pollution|test posiitve)=1008/2416 =0.4172

3)

P(pollution|test negative) =192/7584 =0.0253

pollution present test positive test negative total yes 1008 192 1200 no 1408 7392 8800 total 2416 7584 10000

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