4- Two factories - Factory A and Factory B - design batteries to be used in mobile phones. Factory A produces 60% of all batteries, and Factory B produces the other 40%.2% of Factory A's batteries have defects, and 4% of Factory B's batteries have defects. What is the probability that a battery is both made by Factory A and defective? Show your work. [10 points] 5. Consider the following Bayesian network. Which of the following sentences are true and which ones are False? Briefly justify your answers. [25 points] A. Assuming we know there is rain, whether there is track maintenance does not affect the probability that the train is an time. B. Assuming we know there is track maintenance, whether or not there is rain does not affect the probability that the appointment is attended. C. Assuming we know the train is on time, whether or not there is rain affects the probability that the appointment is attended. D. Assuming we know there is track maintenance, whether or not there is rain does not affect the probability that the train will be on time. E. Assuming we know the train is on time, whether there is track maintenance does not affect the probability that the appointment is attended. 2- Consider the following Bayesian Network. What is the Joint probability of "A does not happen and B happens, and C does not happen, and D happens"? Show your work. [20 points]