Probability and Statistics-Modified Gene A modified gene occurs with probability

Question

Probability and Statistics-Modified Gene A modified gene occurs with probability of 0.5% in the population. There is a test for the modified gene. If a gene is modified, the test always returns a positive. If the gene is not modified, the test returns a false positive 7% of the time. A random gene s tested, and it returns a positive. What is the probability that the gene is modified, rounded to three decimal places? Pick one of the choices 0 0.035% 6.667% 6.698% None of the above Clear selection

Explanation / Answer

Probability of a gene being modified P(M) = 0.005

Probability that the test gives positive given that the gene is modified P(P|M) = 1

Probability that the test gives positive given that the gene is not modified P(P|M') = 0.07

=> P(P and M) = P(P|M) P(M) = 1 * 0.005 = 0.005

P(M') = 1 - 0.005 = 0.995

P(P and M') = P(P|M') P(M') = 0.07 * 0.995 = 0.06965

=> P(P) = P(P and M) + P(P and M') = 0.005 + 0.06965 = 0.07465

P(M|P) = P(M and P) / P(P) = 0.005 / 0.07465 = 0.06698 = 6.698%.

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