Theatre

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 0.006, and the probability that the audio components need repair within 1 year is 0.004. 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.

Help please! On all!

Video bad, P(V) = (.02)
Video good, P(v) = (.98)

Electronics bad, P(E) = (.006)
Electronics good, P(e) = (.994)

Audio bad, P(A) = (.004)
Audio good, P(a) = (.996)

a) at least one component bad. Think of the reverse situation where no component is bad. That would be P(v) = (.98) times P(e) = (.994) times P(a) = (.996):

Probability of everything being okay is

(.98)(.994)(.996) = .9702 approx.

“at least one component bad” is 1 – “no component bad”:

1 - .9702 = .0298 approx.

b) “Exactly one component will need repair” means one bad and the other two good. There are three ways this could happen.

P(V) x P(e) x P(a) = (.02)(.994)(.996) = .0198

P(v) x P(E) x P(a) = ?

P(v) x P(e) x P(A) = ?

Add them up.