If testing is conducted based on the probability of running each path, how many test cases are needed that start from node $1$ and end at node $13$ for $1000$ test cases created to test the entire system. The probabilities to start with node $1$ and node $2$ are $0\mathrm{.}3$ and $0\mathrm{.}7,$ respectively. Recall that p$1+$ p$2+...+$ p $=$ p$/(1-$p$),$ where $0$ p $<1.$ Show computation process only without the need of a calculator.