$7.$ A computer system consists of three critical components: a mother board, a power supply, and a hard disk. The failure times of each component follow an exponential distribution with MTBF as follows. Assume that the computer runs continuously for one year.

MTBF

Mother board $1,000,000$ hrs

Power supply $500,000$ hrs

Hard drive $250,000$ hrs

i$.$ Find the reliability of a computer during the first year.

ii$.$ Find the probability that more than or equal to $2$ computers will fail during the first year. There are $100$ computers in the computer lab.