GO test doubt

Question

https://gateoverflow.in/117681/mock-3-28 Question asked in this link is:

Two CSMA/CD stations are each trying to transmit large files of multiple frames. After each frame is sent, they contend for the channel using the binary exponential back-off algorithm.

The probability that the contention ends in round 3 is _____  (up to 3 decimal points).

why 2/4 * 4/16 * 56/64 = 0.109 is incorrect?

 

Comments

This is standard problem in Tanenbaum book check below link problem 4-

http://omikron.eit.lth.se/ETSN01/ETSN01/tutorials/Tutorial8.pdf but its hard to understand the proof.

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@Utkarsh Joshi what is right answer then ?

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Bikram sir's answer should be right but yet did not get it :(

Answer 1

1) Inititally both stations starts transmitting at random time and get collide , As it is first collsion ,So

For Station 1 ==> (0,2^1 - 1) ==>(0,1)

For Station 2 ==> (0,2^1 - 1) ==>(0,1)

Hence probability of collision in 2nd Try/given that collsion in 1st Try is either 00 /  11 ==> 2/4

2) In second attempt also stations collide .So

For Station 1 ==> (0,2^2 - 1) ==>(0,1,2,3)

For Station 2 ==> (0,2^2 - 1) ==>(0,1,2,3)

Hence probability of NO collision in 3rd Try/given that collision in first 2 try  is  12/16

It is given collsion resolved in 3rd round hence

P(Collsion in 1st round) * P(Collsion in 2nd round) * P(No Collsion in 3rd round)  = 1* 2/4 * 12/16 = 0.375

Here we assumed collsion always occurs in Round 1