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 0.13. Each day, a test is conducted to determine whether the river is polluted by carbon tetrachloride. This test has proved correct 83 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 present 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 percentage of days where the test is negative will the river actually be polluted?

Explanation / Answer

from abvoe:

1)

P(test indicate carbon tetrachloride pollution)=2558/10000=0.26

2)

P(pollution actually exist|test positive)=1079/2558=0.42

3)

% P(actually polluted|test negative)=(221/7442)*100=2.97%

pollution present test +ve test -ve total yes 1079 221 1300 no 1479 7221 8700 total 2558 7442 10000

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