Question $2$: $($You need to do research on this question.$)$

$($a$)$ Define the hypergeometric random variable and explain briefly. $(10$ P$)$

$($b$)$ The components of a $6-$component system are to be randomly chosen from a thousand of $20$ used

components. The resulting system will be functional if at least $4$ of its $6$ components are in working

condition. If $15$ of the $20$ components in the bin are in working condition, what is the probability that

the resulting system will be functional? $($Use the hypergeometric random variable.$)(15$ P$)$