Part B Protein Synthesis A certain gene is necessary for certain protein synthes

Question

Part B Protein Synthesis A certain gene is necessary for certain protein syntheses in human beings. A new kind of test can detect the gene in people who have the gene 99.9% of the time (given the person has the gene), and falsely detects the gene 10.3% of the time (i.e., given the person doesn't have the gene). Suppose 93% of the population carries the gene. 6. (3 marks) What is the probability that a test result indicates the gene is present in a randomly selected person 7. (2 marks) What is the probability that the test is wrong? 8. (2 marks) What is the probability a person has the gene, given the test indicates the person has the gene

Explanation / Answer

Let

G = has the gene
P = positive

6.

P(P) = P(G) P(P|G) + P(G')P(P|G') = 0.93*0.999 + (1-0.93)*0.103 = 0.93628 [ANSWER]

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7.

P(wrong) = P(P n G') + P(P' n G)

= P(G') P(P|G') + P(G) P(P'|G)

= (1-0.93)*0.103 + 0.93*(1-0.999)

= 0.00814 [ANSWER]

***************

8.

P(G|P) = P(G) P(P|G)/P(P) = 0.93*0.999/0.93628

P(G|P) = 0.992299312 [ANSWER]

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