3.20 Bayesian Reasoning for Health Care Testing A pharmaceutical company has dev

Question

3.20 Bayesian Reasoning for Health Care Testing

A pharmaceutical company has developed a potential vaccine against the H1N1 flu virus. Before any testing of the vaccine, the developers assume that with probability 0.5 their vaccine will be effective and with probability 0.5 it will be ineffective. The developers do an initial laboratory test on the vaccine. This initial lab test is only partially indicative of the effectiveness of the vaccine, with an accuracy of 0.6. Specifically, if the vaccine is effective, then this labo- ratory test will return “success” with probability 0.6, whereas if the vaccine is ineffective, then this laboratory test will return “failure” with probability 0.6.

(a) What is the probability that the laboratory test returns “success”?

(b) What is the probability that the vaccine is effective, given that the laboratory test returned “success”?

Answer a and b please

Explanation / Answer

a) probability that the laboratory test returns “success =P(effective and return success+not success and effective success) =0.5*0.6+0.5*0.4=0.5

b)

probability that the vaccine is effective, given that the laboratory test returned “success

P(effective and return success)/P(test return success) =0.5*0.6/0.5 =0.6

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