Let P and Q be two stations arrempting to transmit on an thernet. Each has a steady queue of frames to send. After wach frame is sent(from both sides), they collide for the first time(round 1) and contend for the channel, using the binary exponential backoff algorithm.

What is the probability tha the contention ends on round 4?

Required probability = P(collision at round 1) * P(collision at round 2) * P(collision at round 3) P(No collision at round 4)

= 1/2 + 4/16 + 8/64 + (1 - 16/256)

= 1/2 + 1/4 + 1/8 + 15/16 = 15/1024

The individuals probabilities are calculated based on the fact that, after the i'th collision, a station picks a waiting slot from the interval [0 - (2^i )- 1]

In the given solution they have calculated the required probability as follows

Required probability = 1 * 1/2 * 1/4 * (1-1/8) = 7/64

Looks like here they are assuming that a station picks a waiting slot from the interval [0 - 2^(i-1)], which is wrong, of course.

Am I overlooking something here??