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Message: <blockquote data-quote="question_guy" data-source="post: 2491491" data-attributes="member: 287995">(a) First consider, what's the probability that *no* component will need repair?  That's 1-.01 * 1-.007 * 1-.002 = 0.981.  So the probability that at least one component will require repair is 1 - .981 = 0.019.(b) If the probabilities of failure are p, q, and r, then the probability of exactly one component failing is p(1-q)(1-r) + (1-p)(q)(1-r) + (1-p)(1-r)q.  Note that each of those terms represents a mutually exclusive case: one of the components failing and the other two not failing.  For the specifics of p=.01, q=.007, r=.002, that's .01879.</blockquote>