MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability
Problem
In a factory, every bulb produced passes through two independent defect-detection tests. The visual inspection detects a defective bulb with probability 0.85, while an X-ray test detects a defective bulb with probability 0.90. The outcome of the two tests on any bulb, and across different bulbs, are all independent. A shipment contains 4 defective bulbs which are tested one after another.
(i) Find the probability that none of the 4 defective bulbs is detected by either test.
(ii) Hence calculate the probability that at least one defective bulb is detected by at least one of the two tests.
(iii) Given that at least one defective bulb is detected, determine the probability that the visual inspection detects at least one defective bulb.