$30 %$ of the new cars of a particular model are supplied from a factory $X$, the...
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$30 \%$ of the new cars of a particular model are supplied from a factory $X$, the other $70 \%$ from factory $Y$. $10 \%$ of factory X's production has a major fault, $12 \%$ of factory Y's production has such a fault.
A purchaser's new car has a major fault: what is the probability that it was made at factory $Y$ ?
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