Probability - Dependent Events

A company uses two machines, \(\mathrm{A}\) and \(\mathrm{B}\), to makes boxes. Machines \(\mathrm{A}\) makes \(60 \%\) of the boxes.

\(80 \%\) of the boxes made by machine \(\mathrm{A}\) pass inspection.
\(90 \%\) of the boxes made by machine \(\mathrm{B}\) pass inspection.

A box is selected at random.

1. Find the probability that it passes inspection.[3]
2. The company would like the probability that a box passes inspection to be \(0.87\).
   Find the percentage of boxes that should be made by machine \(\mathrm{B}\) to achieve this.[4]