Electric circuit boards are rated excellent, acceptable, or unacceptable. Suppose that 30% of boards are excellent, 60% are acceptable, and 10% are unacceptable. Further, suppose that 10% of excellent boards fail, 20% of acceptable boards fail and 90% of unacceptable boards fail. (a) What is the probability that a board fails? (b) Given that a board fails, what is the probability that it was rated excellent?