$8.$ Consider three nodes A$,$ B and C on a $\backslash (100\backslash$mathrm$\{$Mbits$\}/\backslash$mathrm$\{$sec$\}\backslash )$ Ethernet. Suppose these three nodes are involved in a collision which is the third collision for A$\text{'}$s frame, fourth collision for B$\text{'}$s frame and second collision for C$\text{'}$s frame. After the collision is detected $($we assume that all nodes detect the collision exactly at the same time$),$ nodes calculate their backoff times according to the binary exponential backoff algorithm.

i$)$ What is the probability that the first transmission after the above collision will be a successful retransmission by C $?$

ii$)$ What is the probability that the first transmission after the above collision will be a collision involving all nodes?

iii$)$ What is the probability that the first transmission after the above collision will be a collision involving only nodes A and B $?$