i$.$ There are only three active stations in a slotted Aloha network: A$,$ B$,$ and C$.$ Each station generates a frame in a time slot with the corresponding probabilities pA $=0\mathrm{.}2,$ pB $=0\mathrm{.}3,$ and pC $=0\mathrm{.}4$ respectively.

Solve for

a$.$ The probability that any station can send a frame in the first slot?

b$.$ The probability that station A can successfully send a frame for the first time in the second slot?

c$.$ The probability that station C can successfully send a frame for the first time in the

third slot?

Ans: