Western Digital gives the rate of non-recoverable read errors per bits read of its 8 TB WD80EFZX hard

drive as less than 1 in 10^14. Suppose such a drive is full. What can you say about the probability of encountering at least one non-recoverable read error while copying the entire drive, based on this information? 

1. Give the exact answer and explain it. Consider that hard drive manufacturers use decimal, not binary prefixes in their capacity specifications, i.e. 1 TB is one trillion 10^12 bytes.
2. Give a decimal approximation of the probability in a. using the calculus fact that 

[1 + (x/n) ]^n ≈ ????^x

for small |????| and large integers n. You may give your answer as a percentage. 

2)

Suppose ???? is the set of integers greater than 1, and ???? is the following relation on ????: ???????????? if and only if ???? and ???? share a prime factor. Answer the following questions and explain your answers.

Is ???? reflexive?

Is ???? anti-symmetric?

Is ???? symmetric?

Is ???? transitive?

3)

Let????=Zand????betherelationdefinedby????=Z × Z− {(????,????)|????∈????}. a. Identify the relation ????.

b. Find ????^2 and prove your answer.  ATTACHMENT PREVIEW

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