Hello aaronrjConsider bottles produced by all three machines. Of these, A produces , B and C each. So in bottles produced by A and B, will come from A and from B.

So, given that the bottles come from A and B, the probability that a given bottle is from A is , and from B . Given that the probabilities that they are rejected are and respectively, the probability that a bottle chosen at random is rejected is:Grandad