III. Only three active stations are in a slotted Aloha network: A$,$ B$,$ and C$.$ Each station generates a frame in a time slot with the corresponding probabilities $p_A=0\mathrm{.}3,p_B=0\mathrm{.}4,$ and $p_C=0\mathrm{.}2,$ respectively.

$6$ Marks

a$)$ What is the probability that any station can send a frame in the first slot?

b$)$ What is the probability that station A can successfully send a frame for the first time in the second slot?

c$)$ What is the probability that station C can successfully send a frame for the first time in the third slot?