Score: 0 of 1 pt 414 of 15 (0 complete) HYV Score: 0%, 0 of 15 pts Life Sci 8.4.

Question

Score: 0 of 1 pt 414 of 15 (0 complete) HYV Score: 0%, 0 of 15 pts Life Sci 8.4.57 Question Help * 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 2,000 adults and finds (by other means) that 3% 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 98% 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? Based on these results, what is the probability of a randomly chosen person having cancer given that the test indicates cancer? person that the testimadicaies cancera

Explanation / Answer

1)

P(test indicate cancer)=P(have cancer and test indicate cancer)+P(not have cancer and test indicate cancer)=0.03*0.98+(1-0.03)*0.01=0.0391

hence P(have cancer given test indicate cancer)

=P(have cancer and test indicate cancer)/P(test indicate cancer)=0.03*0.98/0.0391=0.7519

2)

P(have cancer given test not indicate cancer)

=P(have cancer and test not indicate cancer)/P(test not indicate cancer)

=0.03*(1-0.98)/(1-0.0391)=0.0006

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