Comparing two production plans

A factory uses machines \(A\) and \(B\). Currently, \(60\%\) of its items come from \(A\), and the rest come from \(B\). An item made by \(A\) is defective with probability \(0.02\); an item made by \(B\) is defective with probability \(0.05\). An item is selected at random from the factory’s output.

1. Find the probability that the selected item is defective.[2]
2. The factory proposes making \(80\%\) of its items on \(A\). Assuming the two defect probabilities remain unchanged, calculate the new overall defect probability and decide whether it meets a target of at most \(0.03\).[3]
3. Explain why the proposed calculation may be unreliable if increasing machine A’s workload changes its defect probability.[1]