Mathematics, 05.05.2020 07:47 brodycruce
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 0.007, and the probability that the audio components need repair within 1 year is 0.001. Assuming that the events are independent, find the following probabilities. (Round your answers to four decimal places.)
(a) At least one of these components will need repair within 1 year
(b) Exactly one of these component will need repair within 1 year
Answers: 3
![=1-P(A^{c}\cap B^{c}\cap C^{c})\\=1-[P(A^{c})\times P(B^{c})\times P(C^{c})]\\=1-[(1-0.02)\times (1-0.007)\times (1-0.001)]\\=1-0.97216686\\=0.02783314\\\approx 0.0278](/tpl/images/0635/0023/50496.png)
![=P(A\cap B^{c}\cap C^{c})+P(A^{c}\cap B\cap C^{c})+P(A^{c}\cap B^{c}\cap C)\\=[0.02\times (1-0.007)\times (1-0.001)]+[(1-0.02)\times 0.007\times (1-0.001)]\\+[(1-0.02)\times (1-0.007)\times 0.001]\\=0.02766642\\\approx 0.0277](/tpl/images/0635/0023/44607.png)
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