$(11\%)$ In the CSMA$/$CD protocol, the adapter waits for $K^{**}512$ bit times after a collision, where $K$ is drawn randomly.

a$)$ What is the probability that a node chooses $K=8$ after the $6^{th}$ collision? Suppose that the bandwidth of the Ethernet is $10Mbps,$ then the result $K=8$ corresponds to a delay of how many seconds? $(5\%)$

b$)$ Under the same Ethernet bandwidth, compute the mean delay after the $6^{th}$ collision. $(6\%)$