Gce Model Questions Vol1 2023 Further Mathematics Question 23

A factory produces components of type A (60% of output) and type B (40%). Defect rates are 5% for A and 2% for B. An inspection detects a defect with probability 0.9 for a defective A component and 0.8 for a defective B component; non‑defective components always pass. After a component is randomly selected and *passes* inspection, it is used in a device. If the component is non‑defective, the device fails with probability 0.01 for type A and 0.02 for type B. If the component is defective (but undetected), the device fails with probability 0.5 for type A and 0.7 for type B. What is the probability that the device fails, given that the component passed inspection? Give your answer as a decimal rounded to four significant figures.