RANDOM TEST SERIES

Question

Suppose there are 4 nodes N₁, N₂, N₃ and N₄ are using a slotted ALOHA channel to send their own huge data. When competing all the nodes to transfer their data only one node will get succeeded with a probability P. The time is divided into slots S₁, S₂, S₃ ….and so on. What is probability of N₁ succeeded in slot 5?

1. 4*(1-P)³(P(1-P)³)
2.   P(1-P)³(1-P(1-P)³)
3.   4*P(1-P)³(1-P(1-P)³)
4. 4*P(1-P)³(1-P³(1-P)³)

Comments

Is it a) ??

Answer 1

To win the race probability at each slot= P*(1-P)³ 

and to loss the race probability at each slot= 1- P*(1-P)³   

so till 4 slots it lost = 4 (1- P*(1-P)³ )

and at the fitth slot won the race=P*(1-P)³ 

So ans should be  4* (1- P*(1-P)³ )  P*(1-P)³ =  4*P(1-P)³(1-P(1-P)³)

correct me!

Comments

just explain the first line a little bit

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nodes are 4 so...to win N1=P that means N2,N3,N4 must lost =(1-P)*(1-P)*(1-P)=(1-P)³

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how do u know that it lost till the fourth round.It is nowhere mentioned in the question.