Total probability of passing a quality check for items from two machines and the production share that gives a target probability

A factory makes bottles on two machines, \(A\) and \(B\). Machine \(A\) produces \(60\%\) of the bottles and machine \(B\) produces the rest. Of the bottles from machine \(A\), \(80\%\) pass a quality check, and of the bottles from machine \(B\), \(90\%\) pass the check. One bottle is chosen at random from the factory's output.

1. Find the probability that the chosen bottle passes the quality check.[3]
2. The factory wants the probability that a randomly chosen bottle passes the check to be \(0.87\). Find the percentage of the bottles that machine \(B\) would then need to produce.[4]