Let A and B be two stations attempting to transmit on an Ethernet. Each has a steady queue of frames ready to send; A$\text{'}$s frames will be numbered Al$,$ A$2,$ and so on$,$ and B$\text{'}$s similarly. Let $T=51\mathrm{.}2s$ be the exponential backoff base unit.

Suppose A and B simultaneously attempt to send frame $1,$ collide, and happen to choose backoff times of $0T$ and $1T,$ respectively, meaning A wins the race and transmits $Al$ while B waits. At the end of this transmission, B will attempt to retransmit B$1$ while A will attempt to transmit A$2.$ These first attempts will collide, but now A backs off for either $0T$ or $1T,$ while B backs off for time equal to one of $0T,$dots,$3T.$

Give the probability that A wins this second backoff race immediately after this first collision; that is$,$ A$\text{'}$s first choice of backoff time $k51\mathrm{.}2$ is less than B$\text{'}$s$.$