2.3 Testing Vaccines (10 pts) A pharmaceutical company has developed a potential

Question

2.3 Testing Vaccines (10 pts) A pharmaceutical company has developed a potential vaccine against the H?N? 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 laboratory 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"

Explanation / Answer

answer

a

Let S signify that the test returns achievement and F represent that the test proceeds failure.

Let E represent with the aim of the drug is helpful and let IE represent that the medicine is unproductive.

Then

we comprise:

              P(S) = P(S|E)*P(E) + P(S | IE)*P(IE)

            someplace P(S | E) is the prospect of test returning a success result prearranged that te drug is helpful.           

Similarly,

   other values are definite. Now putting the likelihood values we get:

   P(S) = 0.6*0.5+ 0.4*0.5 = 0.3+ 0.2 = 0.5

   Therefore 0.5 is the obligatory probability here.

b)

likelihood that the vaccine is effective, known that the laboratory test return “success” :

P(E | S)

Using Bayes procedure we have:

P(E | S)P(S) = P(S|E)P(E)

as a result,

P(E | S) ={P(S|E)P(E)/ P(S)

= {0.6*0.5/0.5}

= 0.6

Therefore,

prospect that the vaccine is of use, given that the laboratory test return “success” is 0.6.

This was also sensitive since it is given that the trial done is accurate in the midst of 60% accuracy.

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