Consider an CSMA$/$CA $802\mathrm{.}11$WLAN with three stations: A$,$ B$,$ and C$.$ Node B is the access point and is in full wireless contact with both A and C$.$ The following are the appropriate parameter values for this WLAN $($note: artificial values are used for the WLAN parameters to simplify your calculations$)$

Time slot $=1,$ DIFS $=3,$ SIFS $=1$ Length of RTS$,$ CTS$,$ or ACK $=1$ Initial backoff range for a frame is $[0,7]$

At time t$=0,$ the application layer of station A generated data to be transmitted as a frame of length $10$ destined to B$.$ At that same time $($t$=0),$ the application layer of station C generated data to be transmitted as a frame of length $10$ destined to B$.$ Before transmitting a frame, both node A and node C must wait for DIFS, followed by a random backoff period. The hidden node problem does not exist in this WLAN Note: Clearly indicate the backoff random counter selected by each node and give time charts supporting your answer. Consider all possible scenarios that give the correct solution.

$$ Assume the RTS$/$CTS mechanism is used by all nodes. What is the earliest time T at which both data frames are successfully received and acknowledged by node B$?$ What is the probability that this earliest time is achieved?