Answer Happy

Quiz 2.4 A memory module consists of nine chips. The device is designed with redundancy so that it works even if one of its chips is defective. Each chip contains n transistors and functions properly only if all of its transistors work. A transistor works with probability p independent of any other transistor. (a) What is the probability P[C] that a chip works? (b) What is the probability P[M] that the memory module works? (c) If p = 0.999, what is the maximum number of transistors per chip n that produces P[M] 0.9 (a 90% success probability for the memory module)? (d) If the memory module can tolerate two defective chips, what is the maximum number of transistors per chip n that produces P[M] > 0.9?