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Question B4 (25 marks) A sportswear company produces running watches. Of the watches the sportswear company produce 15% are faulty and malfunction within the warranty period. These products are fixed at a cost (to the company) of 50. Due to the highly priced components within the watch the company prefers to repair watches within the warranty period rather than replace them. In an attempt to lower the number of repairs the quality assurance team suggests performing a full quality inspection to check for faults in the watches before they are sold. Full inspection eliminates the chance of malfunction within the warranty period for final product, but costs 10 per watch. As an alternative to the full inspection the sportswear company are also considering a quick test that costs just 1 per watch. The quick test may be cheaper than the full inspection but it is not guaranteed to detect a faulty product. The outcome of the quick test is either a positive or negative indication that the watch is faulty. To gauge the reliability of the quick test a number of experiments were performed on a set of good and faulty products. This has provided the following conditional probabilities: QUICK TEST RESULTS Positive STATE OF WATCH Good Faulty 0.65 0.2 Negative 0.35 0.8 When the quick test is performed, there remains the option of assembling the device with or without a full inspection. There is also the option of fixing faulty products without any test or inspection due to a watch malfunctioning. a) What is the probability of having a good or faulty final watch given the quick test result? (work to 2 decimal places) (30 % marks)