The transport layer handles the transmission error by requesting the damaged segments to be retransmitted. if the probability of a segment being damaged is p, what is the mean number of the transmissions required to send a segment? you can assume the acknowledgements are never lost for solving this question.

The geometric distribution applies to experiments employing Bernoulli trials (success or failure) to determine the number of trials to obtain the first success.
This distribution may be applied to the given situation, where the probability of success is p.
Let n=number of transmissions required  (n ≥ 1)Then
P(n)=(1-p)^(n-1)*p   (probability that n transmissions are required)
and the mean number of transmissions required
μ = 1/p