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We have installed an alarm at home. At burglary it makes noise by 96% certainty, but also on other nights it can make noise at probability of 0.3% due to disturbances. In our neighborhood there is a burglary chance of 3% on any given night in a given home. Tonight the alarm makes noise, how likely is it that there really is a burglary? I solved it this way, can someone check if i have something wrong. Let B the even that there is a burglary and A that alarm makes noise.

$P(A \mid B) = 0.96,\\ P(B) = 0.03,\\ P(B^C) = (1-0.03)$

$P(A \mid B^C) = 0.003$

$P(B \mid A) = ? ==>$ $\frac{P(A \mid B)P(B)}{P(A \mid B)P(B) + P(A \mid B^C)P(B^C)}$

is this right way or i make mistakes?

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    $\begingroup$ please add self study tag $\endgroup$
    – Haitao Du
    Oct 13, 2016 at 16:33
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    $\begingroup$ this looks right $\endgroup$
    – Matthew Gunn
    Oct 13, 2016 at 17:57
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    $\begingroup$ "In our neighborhood there is a burglary chance of 3% on any given night in a given home." - maybe you should move. :) $\endgroup$
    – Danica
    Oct 14, 2016 at 9:54

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