(c) (10 points) P(AUB) and P(A|B) · (d) (10 points) Let X the numbers of the ope
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(c) (10 points) P(AUB) and P(A|B) · (d) (10 points) Let X the numbers of the operatb le machines Find the probability distribution of the random variable X, ie P(X = x). (30 points) A test for a rare disease has a false positive rate 2% and a false negative rate o that the test is positve and B be an event that the person has the disease. Then P(B-0.5%, P(A Bc) 2% 1%. Suppose that 0.5% of the population have the disease. Let Abe an event and P(AIB) = 99%. . (a) (10 points)Find P(An BC) and P(AC n B). . (b) (8 points) What is the probability that the test is positive P(A)? . (c) (6 points) What is the conditional probability that the person has the disease, given that the test is positive P(B|A)? . (d) (6 points) What is the probability that the test is correct?Explanation / Answer
(c) (10 points) P(AUB) and P(A|B) · (d) (10 points) Let X the numbers of the operatb le machines Find the probability distribution of the random variable X, ie P(X = x). (30 points) A test for a rare disease has a false positive rate 2% and a false negative rate o that the test is positve and B be an event that the person has the disease. Then P(B-0.5%, P(A Bc) 2% 1%. Suppose that 0.5% of the population have the disease. Let Abe an event and P(AIB) = 99%. . (a) (10 points)Find P(An BC) and P(AC n B). . (b) (8 points) What is the probability that the test is positive P(A)? . (c) (6 points) What is the conditional probability that the person has the disease, given that the test is positive P(B|A)? . (d) (6 points) What is the probability that the test is correct?
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