Probability Question: Slotted Aloha

[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?

Relevant Equations

I found a solution which does something like that:
(1-p(A))^4 * P(A).

Can some body please explain me this solution?

Zulfi.

 

[anorlunda]

Can some body please explain me this solution?

Not until you show us your work. How did you derive that solution?

 

[zak100]

Hi,
I got it from internet. I can't understand it. Please guide me.

Zulfi.

 

[anorlunda]

Hi,
I got it from internet. I can't understand it. Please guide me.

Zulfi.

That violates our rules. We are not here to feed you answers. We help you to do your own work. If you have done no work other than an Internet search, then you're not ready to ask for help.

What course are you taking? What background do you have that should prepare you to be able to do that homework? Why would you use the Internet instead of using that background?

 

[zak100]

Probability is my weak point. I can't solve probability questions. That's why I am asking help
Zulfi.

 

[RPinPA]

Describe the whole sequence of events "succeeds for the first time in slot 5".

Once you have a description of the events, you can model them.

What happens at slot 1?
What happens at slot 2?
etc

 

[zak100]

Hi,
Success = P(A)
Failure = 1-P(A)
Slot1= no success= 1-P(A)
Slot2 = no success = 1-P(A)
Slot3 = no success = 1-P(A)
Slot4 = no success = 1-P(A)
Probability from 1 to 4 = (1-P(A))^4
Slot 5 = Success of A but failure of other nodes = P(A) * (1-P(B)) * (1-P(C)) * (1-P(D))

Total probability = (1-P(A))^ 4 * P(A) * (1-P(B)) * (1-P(C)) * (1-P(D))

I think I am very close to the answer. Please tell me how to correct the answer?

Zulfi.

 

[zak100]

Hi,
Still waiting for your correction.

Zulfi.