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(1 point) On any given day, the probability that a large local river is polluted

ID: 3069085 • Letter: #

Question

(1 point) On any given day, the probability that a large local river is polluted by a carbon tetrachloride spill is 0.09. Each day, a test is conducted to determine whether the river is polluted by carbon tetrachloride. This test has proved correct 76 percent of the 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 Test 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 percentage of days where the test is negative will the river actually be polluted?

Explanation / Answer

Thus, we get

1) Proportion of days when test is positive = 2868/10000 = 0.2868

2) P(Pollution exist / Test positive) = P(test positive and pollution exist) / P(Test positive)

= 684/2868

= 0.2385 rounding off to 0.24

3) P(Pollution/test is negative) = P(pollution and test is negative) / P(test is negative)

= 216/7132

= 0.030

Pollution Present Test positive Test Negative Yes 0.09*0.76*10000 0.09*(1-0.76)*10000 No (1-0.09)*(1-0.76)*10000 (1-0.09)*0.76*10000