$($b$)$ A Carrier Sensing Multiple Access $/$ Collision Detection $($CSMA$/$CD$)$ network has

four stations A$,$ B$,$ C$,$ D$.$ Suppose station A needs to transmit a frame after $2^{nd}$

collision, station $B$ needs to transmit a frame after $3^{rd}$ collision, station $C$ needs to

transmit a frame after $4^{th}$ collision, and station $D$ needs to transmit a frame after $5^{th}$

collision, what is the probability that each station will choose a different random

integer value for determining the backoff time?

$(5$ Marks$)$