A medical researcher selects a random sample of 2000 adults and find that 2 perc

Question

A medical researcher selects a random sample of 2000 adults and find that 2 percent have a certain cancer. Each of the 2000 adults are given the test and it indicates cancer in 99% of those who have it and 2 percent of those who don't. Based on these results what is the probability of a randomly chosen person having cancer given the test indicates cancer? Of a person having cancer given that the test Does not indicate cancer A medical researcher selects a random sample of 2000 adults and find that 2 percent have a certain cancer. Each of the 2000 adults are given the test and it indicates cancer in 99% of those who have it and 2 percent of those who don't. Based on these results what is the probability of a randomly chosen person having cancer given the test indicates cancer? Of a person having cancer given that the test Does not indicate cancer Of a person having cancer given that the test Does not indicate cancer

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') = 0.02*0.99 + (1-0.02)*0.02 = 0.0394

Hence,

P(D|P) = P(D) P(P|D)/P(P) = 0.02*0.99/0.0394 = 0.50254 [ANSWER]
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b) What is the probability of a person having cancer given that the test does not indicate cancer?

P(D|P') = P(D) P(P'|D)/P(P') = 0.02*(1-0.99)/(1-0.0394) = 0.0002082 [ANSWER]

DO THUMBS UP ^_^

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