Question $4(20$ points$)$

A three$-$station production line is manufacturing a mechanical component. Any defect that occurs at any of the stations is not detected, and the part continues on for the other downstream operations. The defect rate at station $1$ is $\backslash (5\backslash \%\backslash ),$ at station $2$ is $\backslash (10\backslash \%\backslash ),$ and at station $3$ is $\backslash (7\backslash \%\backslash ).$ A batch of $10,000$ parts is launched through this production line.

$($a$)$ How many defect$-$free units will be produced?

$($b$)$ How many units will have one defect?

$($c$)$ How many units will have two defects?

$($d$)$ How many units will have all three possible defects?

NOTE: Since this is a probabilistic analysis, there is no need to round decimals to whole numbers.