Question

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 0.001. Assuming that the events are independent, what is the probability that exactly one of these component will need repair within 1 year. (Round your answers to four decimal places.)

Answer 1

The probability that the video components don't need repair within 1 year is 1 - 0.02
The probability that the electronic components don't need repair within 1 year is 1 - 0.005
The probability that the audio components don't need repair within 1 year is 1 - 0.001
Let the probability that only the video components need repair within one year = Pv.
Then
\[P _{v}=0.02\times0.995\times0.999=you\ can\ calculate\]
Let the probability that only the electronic components need repair within one year = Pe
Then\[P _{e}=0.005\times0.98\times0.999=you\ can\ calculate\]
Let the probability that only the audio components need repair within one year = Pa
Then\[P _{a}=0.001\times0.98\times0.995=you\ can\ calculate\]
The required probability is then:
\[P _{v}+P _{e}+P _{a}=you\ can\ calculate\]