$2.$Slotted Aloha. Suppose four active nodes$-$nodes A$,$ B$,$ C and D$-$are competing for access to a channel

using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to

transmit in each slot with probability p$.$ The first slot is numbered slot $1,$ the second slot is numbered slot

$2,$ and so on$.$

$($a$)$ What is the probability that node A succeeds for the first time in slot $4?$

$($b$)$ What is the probability that any node $($ either A$,$ B$,$ C or D$)$ succeeds in slot $3?$