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?

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Let d_1,d_2, d_3 be thee mutually exclusive diseases. Let S={s_1,s_2, s_(3 ,),.....,s_6} be the set of observable symptoms of these diseases. For example s_1 is the shortness of breath, s_2 is loss of weight, s_3 is fatigue etc. Suppose a random sample of 10,000 patients contains 3200 patients with disease d_1, 3500 with disease d_2a n d3300 with disease d_3dot Also, 3100 patients with disease d_1, 3300 with disease d_2a n d3000 with disease d_3 show the symptom S. Knowing that the patient has symptom S, the doctor wishes to determine the patients illness. One the basis of this information, what should the doctor conclude?

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