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 0.004. 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

Answer 1

Let V denote the event that the video component needs repair within 1 year.

E denote the event that the electronic component needs repair within 1 year, and

A denote the event that the audio component needs repair within 1 year.

We are given that :

P(V) = 0.02

P(E) = 0.005

P(A) = 0.004

(a)

We are asked to calculate the following probability :

P(atleast one component will need repair within 1 year) = 1 - P(no component will need repair within 1 year)

(b)

P(exactly one component will need repair within 1 year) = P(video component will need repair only) + P(electronic component will need repair only) + P(audio component will need repair only)

= P(V only) + P(E only) + P(A only)

Now,

Similarly,

Also,

For any queries with the solution provided, feel free to comment and ask.

If the solution was helpful to you, don't forget to give it a thumbs up.