A machine has four independent components, three of which fail with prob- ability q = 1 p, and one with probability 1/2. The machine is operational as long as at least two components are working.

(a) What is the probability that the machine will fail? Evaluate this probability for p = 0.4.

(b) If the machine failed, what is the probability that the component which fails with probability 1/2 actually failed.