After k consecutive collisions (with probability p), a station delays retransmission by a random interval uniformly distributed between 0 and 2k , (so the packet is transmitted k+1 times in total).
Number the attempts starting from 1. Attempt i is distributed among 2i−1 slots . Thus, the probability of a collision on attempt i is 1/(2i−1) or 2−(i−1). The probability that the first k-1 attempts will fail is then:
Pk = (1 − 2 −(k−1)) · $· \prod (i=1 to ( k-1)) $ 2 −(i−1) , which can be simplified to:
Pk = (1 − 2 −(k−1)) · 2 − ((k−1)·(k−2)) /2 ,
so, the expected number of rounds is simply: $\sum_{k}^{}$k.Pk
So, the answer is (A)
Ref: http://omikron.eit.lth.se/ETSN01/ETSN01/tutorials/Tutorial8.pdf