Please show all the steps and answer. Thank you! A patient being examined by a d

Question

Please show all the steps and answer. Thank you!

A patient being examined by a doctor may have either symptom A or symptom B or no symptoms. A patient may not have both symptom A and symptom B simultaneously. The probability that a patient has symptom A is 0.05; the probability that a patient has symptom B is 0.25; and the probability that a patient has no symptom is 0.70. The probability that a patient with symptom A is affected with disease Xis 0.95. The probability that a patient with symptom B is affected with disease Xis 0.60. The probability that a patient with no symptoms is affected with disease X is 0.10· +' What is the probability that a patient is affected with disease X? a. b. Given that an individual has disease X. what is the probability that the patient has no symptoms?

Explanation / Answer

P(A)=0.05, P(B)=0.25 and P(no symptom) =0.7

P(X|A)=0.95, P(X|B)=0.6 and P(X| no symptom)=0.1

a) P(X)=P(X|A)*P(A)+P(X|B)*P(B)+P(X|no symptom)*P(no symptom)= 0.95*0.05+0.6*0.25+0.1*0.7=0.2675

b) P(no symptom|X)=P(X|no symptom)*P(no symptom)/P(X)=0.1*0.7/0.2675=0.26168

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