5 to reduce laboratory costs water samples from three

5. To reduce laboratory costs, water samples from three public swimming pools are combined for
one test for the presence of bacteria. Further testing is done only if the combined sample tests
positive. Based on past results, there is a 0.009 probability of finding bacteria in a public
swimming area. Find the probability that a combined sample from three public swimming
areas will reveal the presence of bacteria. Is the probability low enough so that further testing
of the individual samples is rarely necessary?
b. Is the probability low enough so that further testing of the individual samples is rarely
necessary?
6. Explain how to read the notation P(E|F). 7. Let event A = subject is telling the truth and event B = polygraph test indicates that the subject
is lying. Use your own words to translate the notation P( B|A )into a verbal statement.

8. The conditional probability of B given A can be found by _______.
9. The data represent the results for a test for a certain disease. Assume one individual from the
group is randomly selected. Find the probability of getting someone who tests negative, given
that he or she did not have the disease.
The individual actually had the disease
Yes No
Positive 134 18
Negative 10 138
a. The probability is approximately 0.885
10. The table below displays results from experiments with polygraph instruments. Find the
positive predictive value for the test. That is, find the probability that the subject lied, given
that the test yields a positive result.
Did the subject actually lie?
No (did not lie) Yes (did lie)
Positive test results 18 40
Negative test results 34 12
a. The probability is 0.69 (Round to three decimal places as needed.)
11. . 12. The probability that a randomly selected adult in a particular community is a smoker is 18%.
The probability that a randomly selected adult in the community is a smoker, given that the
adult earns more than $75,000 per year, is 18%. Are the events "is a smoker" and "earns more
than $75,000 per year" independent? Explain.