We have designed k-redundant circuits. That is, we have designed a circuit C with n components C1, C2, ..., Cn where C fails only if k or more circuits fail for 1 ≤ k ≤ n. Each of the circuits fails with probability p, and all of them are mutually independent. 1. Determine the probability that exactly j circuits fail. 2. Determine the probability that C fails

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