Also in an earlier problem it mentions that the probability of 2 events happenin

Question

Also in an earlier problem it mentions that the probability of 2 events happening =P(a)*P(b) which is probably relevent in order to do this problem

IS 10 50 90 95 70 .30 70 05 02 05 10 01 01 10 05 40 10 10 05 15 20 01 70 95 95 40 .30 70 .50 50 .05 45 .00 01 02 25 49 50 .155 126 084 020 098 391 126 Y. 45 10 .70 60 20 10 .30 Y. = normal Y,- atrial septal defect without pulmonary stenosis or pulmonary hypertension = ventricular septal defect with valvular pulmonary stenosis = isolated pulmonary hypertension Y,-transposed great vessels = ventricular septal defect without pulmonary hypertension. y, = ventricular septal defect with pulmonary hypertension x, = age 1-20 years old x, = age > 20 years old x, = mild cyanosis easy fatigue = chest pain = repeated respiratory infections x, = EKG axis more than 1 10 n is defined as pulmonary artery pressure 2 systematic arterial pressure.

Explanation / Answer

Here, we need to maximize the Sensitivity of Test(symptoms), which means that we want such symptoms that should be able to give maximum True Positives for a given value of Positives for the disease.

Now, Atrial septal defect without pulmonary stenosis or pulmonary hypetension has a prevalence ofr 0.126 that is 126 in 1000 people have this disease.This is the value of Total Positives for this disease.

We want 2 such symptoms that give maximum True Positives.

True Positives given by any symptom = 126 * Probability of the symptom given the said disease is present

So, Sensitivity = (126* Probability of the symptom given the said disease is present) / 126

To maximize this value, we want a syptom that has high Probability given the said disease is present.

Two such syptoms are: X7 with a probability of 0.70 and (X1 or X2 or X4) with aprobabilty of 0.50

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