Use total probability for two manufacturing machines and solve an inverse mixture proportion.

A company uses two machines, \(A\) and \(B\), to make boxes. Machine \(A\) makes \(60 \%\) of the boxes. \(80 \%\) of the boxes made by machine \(A\) pass inspection. \(90 \%\) of the boxes made by machine \(B\) 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 \(B\) to achieve this.

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