(Solution) - An automobile manufacturer is concerned about a possible recall -(2025 Original AI-Free Solution)

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An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is 0.25probability that a defect is in the brake system, 0.18 in the transmission 0.17 in the fuel system, and 0.40 in some other area.
(a) What is the probability that the defect is the brakes or the fueling system if the probability of defects in both systems simultaneously is 0.15?
(b) What is the probability that there are no defects in either the brakes or the fueling system?