Question: In order for a circuit board to work, seven identical chips must be in working order. To improve reliability, an additional chip is included in the board, and the design allows it to replace any of the seven other chips when they fail.
(a) Find the probability p that the board is working in terms of the probability p that an individual chip is working.
(b) Suppose that ncircuit boards are operated in parallel, and that we require a 99.9% probability that at least one board is working. How many boards are needed?