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Score: 0 of 1 pt 10 of 10 (6 complete) HW Score: 20%, 2 of 10 pts pts to review X Life Sci 7.6.23 | Question Help A new, simple test has been developed to detect a particular type of ca is put into use. A medical researcher selects a random sample of 2.000 adults and finds (by other means) that 1% have this type of cancer. Each of the 2,000 adults is given the test, and it is found that the test indicates cancer in 96% of those who have it and in 2% of those who do not. ncer. The test must be evaluated before it Based on these results, what is the probability of a randomly chosen person having cancer given that the test indicates cancer? Round to three decimal places as needed.) Par

Explanation / Answer

Based on these results, what is the probability of a randomly chosen person having cancer given that the test indicates cancer?

Let

D = has cancer disease
P = tests positive

As by Bayes' Rule,

P(P) = P(D) P(P|D) + P(D') P(P|D') = 0.01*0.96 + (1-0.01)*0.04 = 0.0492

Hence,

P(D|P) = P(D) P(P|D)/P(P) = 0.01*0.96/0.0492 = 0.19512 [ANSWER]

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