Question

Suppose that a certain disease is present in 10% of the population, and that there is a screening test designed to detect this disease if present. The test does not always work perfectly. Sometimes the test is negative when the disease is present, and sometimes it is positive when the disease is absent. The following table shows the proportion of times that the test produces various results.

	Test Is Positive (P)	Test Is Negative (N)
Disease Present (D)	0.06	0.04
Disease Absent (DC)	0.04	0.86

(a)

Find the following probabilities from the table. (Round your answers to two decimal places.)

P(D)

=

P(D^C)

=

P(N|D^C)

=

P(N|D)

=

(b)

Use Bayes' Rule and the results of part (a) to find

P(D|N).

(Round your answer to three decimal places.)

P(D|N) =  

(c)

Use the definition of conditional probability to find

P(D|N).

(Your answer should be the same as the answer to part (b). Round your answer to three decimal places.)

P(D|N) =  

(d)

Find the probability of a false positive, that the test is positive, given that the person is disease-free. (Round your answer to three decimal places.)

(e)

Find the probability of a false negative, that the test is negative, given that the person has the disease.

(f)

Are either of the probabilities in part (d) or part (e) large enough that you would be concerned about the reliability of this screening method? Explain.

Both the probability of a false positive and the probability of a false negative are higher than 0.10 and would cause concern about the reliability of the screening method.The probability of a false negative is higher than 0.10 and would cause concern about the reliability of the screening method. The probability of a false positive is less than 0.10, so it would not cause any concern.    Both the probability of a false positive and the probability of a false negative are less than 0.10, so neither would cause concern about the reliability of the screening method.The probability of a false positive is higher than 0.10 and would cause concern about the reliability of the screening method. The probability of a false negative is less than 0.10, so it would not cause any concern.

Help for the last 3 question！ I don't really understand false positive/negative

Answer 1