The probability that a certain electronic component fails when first used is \(0.10\). If it does not fail immediately, the probability that it lasts for one year is \(0.99\). The probability that a new component will last for one year is:
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Think of this problem like a path on a probability tree diagram. To reach the final destination ("lasts 1 year"), you must traverse the first branch ("survives immediate use", \(0.90\)) and then multiply it by the next branch down that path ("survives 1 year given it worked initially", \(0.99\)).