Medical case histories indicate that different illnesses mayproduce identical sy

Question

Medical case histories indicate that different illnesses mayproduce identical symptoms. Suppose a particular set of symptoms,H, occurs when any one of three illnesses, I1, I2 or I3 occur.Assume that the simultaneous occurrence of more than one of theseillnesses is impossible and that P(I1) = 0.1, P(I2) = .005 andP(I3) = .02. Also note that P(H|I1) = .90, P(H|I2) = .95 andP(H|I3) = .75. Assuming that an ill person exhibits symptoms H,what is the probability that the person has illness I1? Show allwork!

Explanation / Answer

P ( I1 | H ) = ( P (H|I1) P (I1) ) /( P (H|I1)P (I1)+ P (H|I2) P (I2) +P (H|I2) P (I2) ) <bayesformula>
P( I1 | H )= ((.9)(.1)) / ( (.9)(.1) + (.95)(.005) + (.75)(.02))
P( I1 | H)= ((.09))/ ( (.09) + (.00475) + (.015))
P( I1 | H )=(.09)/(.10975)
P( I1 | H ) =.8200455

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