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Assume that X and Y are the only two stations on an Ethernet. Each has a steady queue of frames to send. Both X and Y attempt to transmit a frame, they wait to get the control of channel using binary exponential algorithm. The probability that both were successfully allowed to send the frame on fifth round of the algorithm (assuming every time both X and Y will collide in back-off race till 4th round) is ________.

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I think it will be 15/16.

After four collisions (Since it is given to assume four collision have happened I think we need not consider that probability), each host will choose a number between (0,$2^{4-1}$).

Probability of collision is 1/16 (Both choosing the same number).

Hence probability of success=15/16.
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i think 31/32 will be the ans
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Thanks for noticing, Updated it.

Here they are asking about the fifth iteration. That means we have to find the probability of success in 5th iteration not in 4th iteration.

For K=5, i.e. (0 to 25-1) = (0,31)PT.

So the probability of collision is 1/32 and hence the probability of success will be (1-1/32) = 31/32.