Four stations are trying to transmit frames through a single channel (only one frame per channel). After each frame is sent, they contend for the channel using Binary Exponential Backoff.
After $i$ collisions, each station waits (backs off) for a random number of slots chosen uniformly between 0 and $2^i - 1$: For the first collision, each sender will wait 0 or 1 slot times. After the second collision, the senders will wait anywhere from 0 to 3 slot times (inclusive). After the third collision, the senders will wait uniformly from 0 to 7 slot times (inclusive), and so forth. As the number of retransmission attempts increases, the contention window grows exponentially.
What is the probability of a collision on the i'th attempt?