2. (Conditional Probability) (25 pts) Suppose that during circuit production 1 in 5000 circuits fail. Denote the event that a circuit is faulty by F. A test for the quality circuits yield either negative (-) (i.e., circuit is good) or positive (+) (i.e., circuit is faulty). Suppose that test gives the correct answer 99% of the time. (Hint: P[+(F] = P[-\\F']) (a) (1pts) What is P[F']? (b) (2pts) In words write what the probabilities P[+ ( F] and P[-[F'] mean. (c) (2pts) What are the values of P[+(F] and P[-(F']? (d) (5pts) What are the values of P[-[F] and P[+( F']? (e) (5pts) What is the probability that a circuit tests positive? (Hint: Find P[+]). (f) (5pts) What is the conditional probability that a circuit is faulty given that the test showed +? (g) (5pts) What is the conditional probability that a circuit is faulty given that the test showed -? Instruction: For all questions, provide the answers up to four digits after the decimal point