Problem $1$: Two stations A and B contend for a common medium using a slotted time system with a slot duration

of one unit of time. A packet from either A or B can be sent and be received to C or D$,$ respectively in one time

slot. Each station attempts to transmit on a given time slot independently with probability p$.$ If a collision occurs,

each station retries on the next time slot with the same probability p$.$

$($a$)$ What is the probability of success on any one slot?

$($b$)$ What is the probability of experiencing k consecutive collisions?

$($c$)$ What is the expected number of transmission attempts needed for one success from either A or B$?$