Question 852762: Hello. The problem I need help on is a probability one. The problem is:
In a home theater system, the probability that the video components need repair within 1 year is 0.02, the probability that the electronic components need repair within 1 year is 0.005, and the probability that the audio components need repair within 1 year is 0.002. Assuming that the events are independent, find the following probabilities:
(a) At least one of these components will need repair within 1 year:
I've figured this out by taking the compliments of each probability and got .0269 which is correct.
The second part is what I need help on.
(b) Exactly one of these component will need repair within 1 year:
? I tried solving by taking the compliment of the first one multiplied by the compliment of the second added to the compliment of the second multiplied by the third and then added to the compliment of the first multiplied by the first, but it's not right. I also tried that with the original probabilities given, but that didn't work either. I'm completely stuck. Some help would be appreciated. Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a home theater system, the probability that the video components need repair within 1 year is 0.02, the probability that the electronic components need repair within 1 year is 0.005, and the probability that the audio components need repair within 1 year is 0.002. Assuming that the events are independent, find the following probabilities:
(a) At least one of these components will need repair within 1 year:
I've figured this out by taking the compliments of each probability and got .0269 which is correct.
The second part is what I need help on.
(b) Exactly one of these component will need repair within 1 year:
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P(none need repair) = 0.98*0.995*0.998 = 0.973
P(all need repair) = 0.02*0.005*0.002 = 0.0000002
P(exactly one needs repair = 0.02*0.995*0.998 + 0.005*0.98*0.998 + 0.002*0.98*0.995 = 0.0267..
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Cheers,
Stan H.
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