# probability question

#### cmelliott

##### New member
The chance that doctor A will diagnose disease X correctly is 60%. The chance that a patient will die by his treatment after a correct diagnosis is 40% and the chance of death by wrong diagnosis is 70%. A patient of doctor A, who had disease X died. What is the chance that his disease was diagnosed correctly?

#### tkhunny

##### Moderator
Staff member
A tree might help.

Has the disease. This is not disputed.

Correct Diagnosis 60% -- No Correct Diagnosis 40%

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Now, consider just the Correct Diagnosis: (60%)

Death any way: 40% (I presume you don't actually mean that the treatment itself killed the patient.) -- Survival: 60%

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Now, consider just the Missed Diagnosis: (40%)

Death: 70% -- Survival: 30%

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So, what do we know and how can we answer the question? Bayes might help.