Answer :

Given:


1800 patients had disease d1


2100 patients had disease d2


1100 patients had disease d3


Let us assume U1, U2, U3 and A be the events as follows:


U1 = Person with disease d1


U2 = Person with disease d2


U3 = Person with disease d3


A = Showing the symptom S


Now,





P(A|U1) = P(patient who has disease d1 showed the symptom S)




P(A|U2) = P(patient who has disease d2 showed the symptom S)




P(A|U3) = P(patient who has disease d3 showed the symptom S)




Now we find


P(U1|A) = P(The patient who showed symptom S has disease d1)


P(U2|A) = P(The patient who showed symptom S has disease d2)


P(U3|A) = P(The patient who showed symptom S has disease d3)


Using Baye’s theorem:

















Since the probability of P(U1|A) is larger than other disease’s probability. The patient mostly likely to have the disease d1.


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