Exercise 3 - Bayes' Rule in the Courtroom

Many press reports stated that the expert claimed the probability of Sally Clark being innocent as 1 in 73 million. Perhaps the jury and judge also interpreted the testimony this way. This probability can be written like this:

$$ \mbox{Pr}(\mbox{mother is a murderer} \mid \mbox{two children found dead with no evidence of harm}) $$

Bayes' rule tells us this probability is equal to:

Possible Answers

$$\frac{\mbox{Pr}(\mbox{two children found dead with no evidence of harm}) \mbox{Pr}(\mbox{mother is a murderer})}{\mbox{Pr}(\mbox{two children found dead with no evidence of harm})}$$
$\mbox{Pr}(\mbox{two children found dead with no evidence of harm})\mbox{Pr}(\mbox{mother is a murderer} )$
$$\frac{\mbox{Pr}(\mbox{two children found dead with no evidence of harm} \mid \mbox{mother is a murderer} ) \mbox{Pr}(\mbox{mother is a murderer})}{\mbox{Pr}(\mbox{two children found dead with no evidence of harm})}$$
1/8500

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