Simplest Diagnostic Case

• Suppose know Alarm ringing & want to know: Burglary?

• I.e. want P(B|A)

P(B|A) =P(A|B) P(B) / P(A)

But we don’t know P(A)

1 =P(B|A)+P(~B|A)

1 =P(A|B)P(B)/P(A) + P(A|~B)P(~B)/P(A)

1 =[P(A|B)P(B) + P(A|~B)P(~B)] / P(A)

P(A) =P(A|B)P(B) + P(A|~B)P(~B)

P(B | A) =P(A|B) P(B) / [P(A|B)P(B) + P(A|~B)P(~B)]

= .95*.001 / [.95*.001 + .01*.999] = 0.087

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