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Answer:
a)
b)
c) n=62
d) n=138
Step-by-step explanation:
Note: "Each chip contains n transistors"
a) A chip needs all n transistor working to function correctly. If p is the probability that a transistor is working ok, then:
b) The memory module works with when even one of the chips is defective. It means it works either if 8 chips or 9 chips are ok. The probability of the chips failing is independent of each other.
We can calculate this as a binomial distribution problem, with n=9 and k≥8:
c)
This equation was solved graphically and the result is that the maximum number of chips to have a reliability of the memory module equal or bigger than 0.9 is 62 transistors per chip. See picture attached.
d) If the memoty module tolerates 2 defective chips:
We again calculate numerically and graphically and determine that the maximum number of transistor per chip in this conditions is n=138. See graph attached.
r=common ratio: 12/6=2; 6/3=2
r=2,
plug in 12 for n:
The twelfth term in the sequence is 6144