Many email account hoders get spam email inviting the purchase of certain drugs.

Question

Many email account hoders get spam email inviting the purchase of certain drugs.such drugs have to be approved by FDA in USA before sale. Suppose there is a 0.95 chance the FDA will approve anew drug if the results of current testing show no side effects, but they will also approve the drug with a 0.50 chance if testing shows side effects.A certain physician working fro the drug manufacturer believes there is a 0.20 chance the drug will cause side effects. What is the probability the drug will be approved by the FDA?

Explanation / Answer

P(approve | no side effects)=0.95

P(approve | side effects)=0.5

P(side effects)=0.2 therefore P(no side effects)=1-0.2=0.8

thus P(approve)=P(approve | no side effects)*P(no side effects)+P(approve | side effects)*P(side effects) = 0.95*0.8+0.5*0.2=0.86

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