Chapter4Q05answer1[1] - = 0.83 v) 40 cars have faulty...

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Chapter 4 Question 5 Condition of brakes Condition of tires Faulty Not faulty Total Faulty 25 5 30 Not faulty 15 55 70 Total 40 60 100 a) i) p (faulty brakes) = 30/100 = 0.30 ii) p (faulty tires) = 40/100 = 0.40 iii) p (either faulty brakes or faulty tires) = p (faulty brakes) + p (faulty tires) – p (faulty brakes and faulty tires) = 40/100 + 30/100 – 45/100 = 25/100 = 0.25 iv) 30 cars have faulty tires. Of these cars, 25 have faulty brakes, so p (car has faulty brakes given that it has faulty tires) = 25/30
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Unformatted text preview: = 0.83 v) 40 cars have faulty brakes. Of these cars, 25 have faulty tires, so p (car has faulty tires given that it has faulty brakes) = 25/40 = 0.63 b) Since the probability of faulty tires increases if a car has faulty brakes – from 0.40 to 0.63 – it appears that the two events are dependent. However, we can only draw this conclusion tentatively as our evidence is based on a sample of only 100 cars....
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