Mineral Economics, Mine Planning, Systems Engineering · Systems Engineering · 1 mark · Numerical answer
A safety device has independent critical components with failure probabilities 0.2 and 0.1. Failure of either or both can cause an accident. Find accident probability to two decimals.
An accident is avoided only if both components work. Independence gives P(no failure)=0.8×0.9=0.72. Therefore accident probability is 1−0.72=0.28. Equivalently, union probability is 0.2+0.1−0.2×0.1; simply adding would count simultaneous failure twice.
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