7) Given the test result of cancer test below. If one subject is randomly select
ID: 3050192 • Letter: 7
Question
7) Given the test result of cancer test below. If one subject is randomly selected, Positive Negative Find the probability that one subject has cancer. Subject Test Test b) What does P(Negative | has cancer) means? Find the probability. Is this situation good? -result result has cancer 8 No Cancer 99 891 b) find the probability that one subject has cancer given that the test result is positive. Does result increase the chance of a subject having cancer? c) Find the proba bility that a subject will get positive test result given that the subject has cancer. d) Find the probability that a subject has negative test result or no cancer.Explanation / Answer
Total subjects = 8 + 2 + 99 + 891 = 1000
A) P(subject has cancer) = (8 + 2) / 1000 = 0.01
B) It mean that the randomly selected subject test result is negative given that subject has cancer.
P(negative test result | has cancer) = P(negative test result and has cancer) / P(has cancer)
= (2/1000) / (10/1000)
= 2 / 10
= 0.2
No this situation is not good.
B) P(has cancer | test result is positive) =P(has cancer and test result is positive) / P(test result is positive)
= (8/1000) / ((8+99)/1000)
= 8 / 107
= 0.0748
C) P(test positive | has cancer) = P(test positive and has cancer) / P(has cancer)
= (8/1000) / (10/1000)
= 8/10
= 0.8
D) P(negative test result or no cancer) = P(negative test result) + P(no cancer) - P(negative test result and no cancer)
= (2+891)/1000 + (99+891)/1000 - 891/1000
= 992/1000
= 0.992
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