Let `d1, d2, d3` be three mutually exclusive diseases. Let `S` be the set of observable symptoms of these diseases. A doctor has the following information from a random sample of `5000` patients: `1800` had disease `d1`, `2100` has disease `d2` and the others had disease `d3`. `1500` patients with disease `d1`, `1200` patients with disease `d2`and `900` patients with disease `d3` showed the symptom. Which of the diseases is the patient most likely to have?

Explanation

Let, `A =` having symptom `S`


`E_1 =` having disease `d1`


`E_2 =` having disease `d2`


`E_3 =` having disease `d3`


Given,


`P(E_1) =1800/5000`


`P(E_2) =2100/5000`


`P(E_3) =1100/5000`


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