Refer to problem $1.$ Let W be the event that the donor is White, B be the event the donor is Black, and A be the event the donor is Asian. Let T$1$ be the event that the donor is Type O$,$ T$2$ be the event that the donor is Type A$,$ T$3$ be the event that the donor is Type B$,$ and T$4$ be the event that the donor is Type AB$.$

$($a$)$ Describe in words the event T$1|$ W$.$

$($b$)$ Compute the probability of the occurrence of the event T$1|$ W$,$ P$($T$1|$ W$).$

$($c$)$ Are the events T$1$ and W independent? Justify your answer.

$($d$)$ Are the events T$1$ and W mutually exclusive? Justify your answer.