$1.($A$)$ On a disk system with: a data block $($consecutive sectors which is the access unit$)$ size is $4$

Kbytes, RPM is $7200,$ average seek time is $3$ msec, and the data transfer rate is $20$ MB$/$s$,$ what is

the access time to read a data block at a random location? If the data block size is $64$ Mbytes,

what would be the access time? $($C$)$ If a disk system contains $1,000$ disk drives $($uniquely numbered as HID $0001$ HID$1000),$ and the

probability of an individual disk failure is $1/100,000.$ What will be the probability that the

system experiences any disk failure? Note that failures happen independently. $($D$)$ In the same system as described in c$),$ two copies of a data block are stored in HID$200$ and

HID$300.$ What is the probability that the system loses the data block due to the concurrent

failure of HID$200$ and HID$300?$