An Ethernet switch is simply a bridge that has the ability to forward some number of packets in parallel, assuming the input and output ports are all distinct. Suppose two such N-port switches, for a large value of N, are each able to forward individually up to three packets in parallel. They are then connected to one another in series by joining a pair of ports, one from each switch; the joining link is the bottleneck as it can, of course, carry only one packet at a time.

(a) Suppose we choose two connections through this combined switch at random. What is the probability that both connections can be forwarded in parallel? Hint: This is the probability that at most one of the connections crosses the link.

(b) What if three connections are chosen at random?