In proof testing of circuit boards, the probability that any particular diode will fail is . suppose a circuit board contains diodes. how many diodes would you expect to fail, and what is the standard deviation of the number that are expected to fail? what is the (approximate) probability that at least four diodes will fail on a randomly selected board? if five boards are shipped to a particular customer, how likely is it that at least four of them will work properly? (a board works properly only if all its diodes work.)