A computer network shown in Fig. $1$ connects two nodes A and $B$ through intermediate nodes $C,D,E,$ and $F.$ The probabilities associated with each connection are $p_{AD}=0\mathrm{.}75,p_{AC}=0\mathrm{.}9,p_{CE}=0\mathrm{.}8,p_{CF}=0\mathrm{.}95,p_{EB}=0\mathrm{.}9,p_{FB}=0\mathrm{.}85,$ and $p_{DB}=0\mathrm{.}95.$ What is the probability that there is a connection between A and $B?$

c$.$ Write a MATLAB simulator to verify your answer.

Figure $1$: Computer Network