Using Bayes' theorem setup: P(Disease)=0.01P(Disease) = 0.01P(Disease)=0.01, P(Test+∣Disease)=0.95P(Test+|Disease) = 0.95P(Test+∣Disease)=0.95, P(Test+∣noDisease)=0.05P(Test+|no Disease) = 0.05P(Test+∣noDisease)=0.05. Identify the formula for P(Disease∣Test+)P(Disease|Test+)P(Disease∣Test+).
P(Test+∣Disease)×P(Disease)P(Test+)\frac{P(Test+|Disease) \times P(Disease)}{P(Test+)}P(Test+)P(Test+∣Disease)×P(Disease) where P(Test+)=P(Test+∣Disease)P(Disease)+P(Test+∣noDisease)P(noDisease)P(Test+) = P(Test+|Disease)P(Disease) + P(Test+|no Disease)P(no Disease)P(Test+)=P(Test+∣Disease)P(Disease)+P(Test+∣noDisease)P(noDisease)
P(Test+∣Disease)×P(Disease)P(Test+|Disease) \times P(Disease)P(Test+∣Disease)×P(Disease)
0.95
P(Disease)×P(Test+)P(Disease) \times P(Test+)P(Disease)×P(Test+)