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A new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use.

A​ new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcher selects a random sample of 1,000 adults and finds​ (by other​ means) that 2​% have this type of cancer. Each of the 1,000 adults is given the​ test, and it is found that the test indicates cancer in 99​% of those who have it and in 1​% of those who do not. Based on these​ results, what is the probability of a randomly chosen person having cancer given that the test indicates​ cancer? Of a person having cancer given that the test does not indicate​ cancer?

  1. Based on these​ results, what is the probability of a randomly chosen person having cancer given that the test indicates​ cancer?
  2. What is the probability of a person having cancer given that the test does not indicate​ cancer?

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