Slotted Aloha: Another probability question

[zak100]

Homework Statement

Suppose four active nodes – nodes A, B, C and D – are competing for access to a channel using slotted ALOHA. Assume each node ha 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. What is the probability that node A succeeds for the first time in slot 5?
What is the probability that some node (either A, B, C or D) succeeds in slot 3?

Relevant Equations

Probability equation of failure

Hi,
probability that one node succeeds = p
probability that one node does not succeed = (1-p)
probability that 3 nodes do not succeed = (1-p) ^3
Total probability = probability that one node succeeds * probability that 3 nodes do not succeed

Total probability = p(1-p)^3

Is it correct?

Zulfi.

 

[zak100]

Hi,
p(A succeeds in slot 3) = p(1-p) ^3
p(B succeeds in slot 3) = p(1-p) ^3
p(C succeeds in slot 3) = p(1-p) ^3
p(D succeeds in slot 3) = p(1-p) ^3
= 4p(1-p)^3

Same answer for slot 4?

Please tell me which answer is correct, this one or the previous one?
What about 4 sots?
Zulfi.