Question

A doctor knows that 90% of patients have flu and 10% have allergy. Rash appears in 8% of flu patients and in 95% of allergic ones. If a patient shows rash, what is the probability they have an allergy?

Q: Answer-A doctor knows that 90% of patients have flu and 10% have allergy. Rash appears in 8% of flu patient...

Let the events be F patient has flu PF 0.90 A patient has allergy PA 0.10 R patient shows rash Conditional probabilities PR F 0.08 PR A 0.95 We are asked to find PA R Probability that a patient has allergy given that they have rash Apply Bayes Theorem PA R PA PR A PR Where PR PF PR F PA PR A 0.90 0.08 0.10 0.95 0.072 0.095 0.167 Now plug into Bayes formula PA R 0.10 0.95 0.167 0.095 0.167 0.568