Consider a network with two links.
Node $\text{A}$ is trying to send packets to node $\text{C}.$
Let $p 1$ be the probability of failure on the first link $\text{(A-B)}$, and $p2$ be the probability of failure on the second link $\text{(B-C)}.$
Assume failures are detected by the ends (i.e., $\text{A}$ finds out that the packet did not reach $\text{C}$, and resends). On average, how many transmissions from $\text{A}$ are needed before the packet arrives at the destination $\mathrm{C}?$
A. $\dfrac{p_1 p_2}{\left(1-p_2\right)\left(1-p_1\right)}$
B. $\dfrac{1}{p 1+(1-p 1) p 2}$
C. $\dfrac{p_1}{1-p_1}+\dfrac{p_2}{1-p_2}$
D. $\dfrac{1}{\left(1-p_1\right)\left(1-p_2\right)}$
