In a home theater system, the probability that the video components need...

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NareshAlagan

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...repair within 1 year is 0.01? the probability that the electronic components need repair within 1 year is 0.007, and the probability that the audio components need repair within 1 year is 0.002. Assuming the events are independent, find the following probabilities. (Round your answers to four decimal places.)

(a) At least one component will need repair within 1 year.


(b) Exactly one component will need repair within 1 year.
 
(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.
 
(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.
 
(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.
 
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