There are $3$ production lines in a factory. $2$ of them are new lines and $1$ of them is an old line. All production lines produce at the same rate. The old production line has $8\%$ defective rate while the new production lines have only $3\%$ defective rate. The components are shipped to customers in $100$-unit lots. A buyer received a lot and tested $5$ components and $1$ of it failed.
I want to find the probability that this lot that the buyer had bought was produced by the old line and also the probability that this lot was produced by one of the new lines.
I let the production lines be $A$, $B$ and $C$. Line $C$ is the old one. I also let $D$ be the defective rate. So, I believe the info are given as $P(D|C)=0.08$, $P(D|A)=0.03$ and $P(D|B)=0.03$.
But I am stuck right after this. I don't understand how I should use the $100$ units and $1$ out of $5% tested units in a lot failed.
How should I carry on to find out the probability that the lot that the buyer had bought was produced by the old line and also the probability that the lot that the buyer had bought was produced by one of the new lines?