$3.(20$ pts$)$ Answer the following questions in a disk system with multiple hard disks: a$)$ 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 $($i$.$e$.,$ any one disk fails$)?$ Note that failures happen independently. b$)$ In the same system as described in a$),$ 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$300?$