Can someone point out the mistake. what am I doing wronge? Answer should be the same using both approachesA machine is made up of two components, A and B. Each component either works or fails. The failure or non-failure of one component is independent of the failure or non-failure of the other component. The machine works if at least one of the components works. If the probability that each component works is 2/3, what is the probability that the machine works?
Prob that neither component works = 1/3*1/3
Prob that machine works = 1- 1/9 = 8/9
Prob Machine works = Prob (A works) * Prob (B does not work) + Prob (B works) * Prob (A does not work)
= 2/3*1/3 + 2/3*1/3
= 2/9 + 2/9 = 4/9
Prob that neither component works = 1/3*1/3
Prob that machine works = 1- 1/9 = 8/9
Prob Machine works = Prob (A works) * Prob (B does not work) + Prob (B works) * Prob (A does not work)
= 2/3*1/3 + 2/3*1/3
= 2/9 + 2/9 = 4/9
