The probabilities of poor print quality given no printer problems, misalligned paper, high Ink viscosity, or printer$-$head debris are $0,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}6,$ respectively. The probabilities of no printer problems, misaligned paper, high ink viscosity, or printer$-$head debris are $0\mathrm{.}8,0\mathrm{.}02,0\mathrm{.}08,0\mathrm{.}1,$ respectively.

$($a$)$ Determine the probability of printer$-$head debris, given poor print quality. $(2$ marks$)$

$($b$)$ Given poor print quality, is misaligned paper or high ink viscosity more likely? $(2$ marks$)$

$($c$)$ What is the probability of encountering good print quality? $(2$ marks$)$

$($d$)$ What is the probability of encountering printer$-$head debris or high ink viscosity? $(2$ marks$)$

$($e$)$ Show that printer$-$head debris and poor print quality are not independent. $(2$ marks$)$