Answer Happy

Let A = the unconditional probability that the government
approves the drug if the company does not conduct any
experiment.
Let B = the unconditional probability that the government
will approve the drug if the company conducts its optimal
experiment.
B - A = ?
(Please round your answer to three decimal places if it
contains a fraction.)
A pharmaceutical company has developed a new drug. The government will approve this drug if and only if the probability that it has negative side effects is lower than or equal to 0.05. The common prior belief is Pr(negative side effects) = 0.2. The company does not know the true probability of side effects; it is responsible to conduct a lab experiment that provides information on this probability. The company can choose its own design of this experiment, but it must truthfully reveal the design and the result of the experiment to the government. A design of the experiment can be described by the conditional probabilities Pr(pass/negative side effects) and Pr(pass no negative side effects). Without loss of generality, assume that Pr(pass negative side effects) < Pr(pass|no side effects). The government observes these condition probabilities as well as the experiment outcome (pass or fail). It Bayesian updates its posterior belief base on information and approves the drug if Pr(negative side effects)<=0.05.